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{\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{red}{t}}_{4} & {\\color{red}{t}}_{5} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 8 & 0 & 3 & 7 & 1 & 0 & 0 & 6 & 0 & 0 & -6 & 0 & 18800 \\\\\n", "{\\color{green}{s}}_{2} & 6 & 0 & 2 & 8 & 0 & 1 & 0 & 5 & 0 & 0 & -5 & 0 & 15000 \\\\\n", "{\\color{green}{s}}_{3} & 5 & 0 & 2 & 6 & 0 & 0 & 1 & 4 & 0 & 0 & -4 & 0 & 13200 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 200 \\\\\n", "{\\color{red}{t}}_{5} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 400 \\\\\n", "{\\color{green}{s}}_{6} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 500 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 400\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 t4 t5| rhs]\n", "[-----+-----------------------------------------------------------------------+-----]\n", "[ s1| 8 0 3 7 1 0 0 6 0 0 -6 0|18800]\n", "[ s2| 6 0 2 8 0 1 0 5 0 0 -5 0|15000]\n", "[ s3| 5 0 2 6 0 0 1 4 0 0 -4 0|13200]\n", "[ x2| 0 1 0 0 0 0 0 -1 0 0 1 0| 200]\n", "[ t5| 0 0 1 0 0 0 0 0 -1 0 0 1| 400]\n", "[ s6| 0 0 0 1 0 0 0 0 0 1 0 0| 500]\n", "[-----+-----------------------------------------------------------------------+-----]\n", "[ W| 0 0 -1 0 0 0 0 0 1 0 1 0| 400]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 5 , 3 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{red}{t}}_{4} & {\\color{red}{t}}_{5} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 8 & 0 & 0 & 7 & 1 & 0 & 0 & 6 & 3 & 0 & -6 & -3 & 17600 \\\\\n", "{\\color{green}{s}}_{2} & 6 & 0 & 0 & 8 & 0 & 1 & 0 & 5 & 2 & 0 & -5 & -2 & 14200 \\\\\n", "{\\color{green}{s}}_{3} & 5 & 0 & 0 & 6 & 0 & 0 & 1 & 4 & 2 & 0 & -4 & -2 & 12400 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 400 \\\\\n", "{\\color{green}{s}}_{6} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 500 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{red}{t}}_{4} & {\\color{red}{t}}_{5} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 8 & 0 & 0 & 7 & 1 & 0 & 0 & 6 & 3 & 0 & -6 & -3 & 17600 \\\\\n", "{\\color{green}{s}}_{2} & 6 & 0 & 0 & 8 & 0 & 1 & 0 & 5 & 2 & 0 & -5 & -2 & 14200 \\\\\n", "{\\color{green}{s}}_{3} & 5 & 0 & 0 & 6 & 0 & 0 & 1 & 4 & 2 & 0 & -4 & -2 & 12400 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 400 \\\\\n", "{\\color{green}{s}}_{6} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 500 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 t4 t5| rhs]\n", "[-----+-----------------------------------------------------------------------+-----]\n", "[ s1| 8 0 0 7 1 0 0 6 3 0 -6 -3|17600]\n", "[ s2| 6 0 0 8 0 1 0 5 2 0 -5 -2|14200]\n", "[ s3| 5 0 0 6 0 0 1 4 2 0 -4 -2|12400]\n", "[ x2| 0 1 0 0 0 0 0 -1 0 0 1 0| 200]\n", "[ x3| 0 0 1 0 0 0 0 0 -1 0 0 1| 400]\n", "[ s6| 0 0 0 1 0 0 0 0 0 1 0 0| 500]\n", "[-----+-----------------------------------------------------------------------+-----]\n", "[ W| 0 0 0 0 0 0 0 0 0 0 1 1| 0]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "El problema de la fase I es óptimo y Wopt=0. Por tanto, el original es factible\n", "Preparemos el cuadro inicial de la fase II\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\ \\ \\ Fase\\ II}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\ \\ \\ Fase\\ II}$$" ], "text/plain": [ "FII" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " 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{x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 8 & 0 & 0 & 7 & 1 & 0 & 0 & 6 & 3 & 0 & 17600 \\\\\n", "{\\color{green}{s}}_{2} & 6 & 0 & 0 & 8 & 0 & 1 & 0 & 5 & 2 & 0 & 14200 \\\\\n", "{\\color{green}{s}}_{3} & 5 & 0 & 0 & 6 & 0 & 0 & 1 & 4 & 2 & 0 & 12400 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 400 \\\\\n", "{\\color{green}{s}}_{6} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n", "\\hline\n", " {Z_{ind}} & 1750 & 0 & 0 & 2000 & 0 & 0 & 0 & 1200 & 700 & 0 & 520000\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n", "[------+---------------------------------------------------------------------+------]\n", "[ s1| 8 0 0 7 1 0 0 6 3 0| 17600]\n", "[ s2| 6 0 0 8 0 1 0 5 2 0| 14200]\n", "[ s3| 5 0 0 6 0 0 1 4 2 0| 12400]\n", "[ x2| 0 1 0 0 0 0 0 -1 0 0| 200]\n", "[ x3| 0 0 1 0 0 0 0 0 -1 0| 400]\n", "[ s6| 0 0 0 1 0 0 0 0 0 1| 500]\n", "[------+---------------------------------------------------------------------+------]\n", "[ Z| 1750 0 0 2000 0 0 0 1200 700 0|520000]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 6 , 4 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 8 & 0 & 0 & 0 & 1 & 0 & 0 & 6 & 3 & -7 & 14100 \\\\\n", "{\\color{green}{s}}_{2} & 6 & 0 & 0 & 0 & 0 & 1 & 0 & 5 & 2 & -8 & 10200 \\\\\n", "{\\color{green}{s}}_{3} & 5 & 0 & 0 & 0 & 0 & 0 & 1 & 4 & 2 & -6 & 9400 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 400 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n", "\\hline\n", " {Z_{ind}} & 1750 & 0 & 0 & 0 & 0 & 0 & 0 & 1200 & 700 & -2000 & 1520000\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 8 & 0 & 0 & 0 & 1 & 0 & 0 & 6 & 3 & -7 & 14100 \\\\\n", "{\\color{green}{s}}_{2} & 6 & 0 & 0 & 0 & 0 & 1 & 0 & 5 & 2 & -8 & 10200 \\\\\n", "{\\color{green}{s}}_{3} & 5 & 0 & 0 & 0 & 0 & 0 & 1 & 4 & 2 & -6 & 9400 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 400 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n", "\\hline\n", " {Z_{ind}} & 1750 & 0 & 0 & 0 & 0 & 0 & 0 & 1200 & 700 & -2000 & 1520000\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n", "[-------+-------------------------------------------------------------------------------+-------]\n", "[ s1| 8 0 0 0 1 0 0 6 3 -7| 14100]\n", "[ s2| 6 0 0 0 0 1 0 5 2 -8| 10200]\n", "[ s3| 5 0 0 0 0 0 1 4 2 -6| 9400]\n", "[ x2| 0 1 0 0 0 0 0 -1 0 0| 200]\n", "[ x3| 0 0 1 0 0 0 0 0 -1 0| 400]\n", "[ x4| 0 0 0 1 0 0 0 0 0 1| 500]\n", "[-------+-------------------------------------------------------------------------------+-------]\n", "[ Z| 1750 0 0 0 0 0 0 1200 700 -2000|1520000]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 2 , 1 )\n" ] }, { "data": { "text/html": [ " 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4495000\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 0 & 0 & 0 & 1 & -\\frac{4}{3} & 0 & -\\frac{2}{3} & \\frac{1}{3} & \\frac{11}{3} & 500 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & \\frac{1}{6} & 0 & \\frac{5}{6} & \\frac{1}{3} & -\\frac{4}{3} & 1700 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & 0 & -\\frac{5}{6} & 1 & -\\frac{1}{6} & \\frac{1}{3} & \\frac{2}{3} & 900 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 400 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & 0 & -\\frac{875}{3} & 0 & -\\frac{775}{3} & \\frac{350}{3} & \\frac{1000}{3} & 4495000\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n", "[-------+-------------------------------------------------------------------------------+-------]\n", "[ s1| 0 0 0 0 1 -4/3 0 -2/3 1/3 11/3| 500]\n", "[ x1| 1 0 0 0 0 1/6 0 5/6 1/3 -4/3| 1700]\n", "[ s3| 0 0 0 0 0 -5/6 1 -1/6 1/3 2/3| 900]\n", "[ x2| 0 1 0 0 0 0 0 -1 0 0| 200]\n", "[ x3| 0 0 1 0 0 0 0 0 -1 0| 400]\n", "[ x4| 0 0 0 1 0 0 0 0 0 1| 500]\n", "[-------+-------------------------------------------------------------------------------+-------]\n", "[ Z| 0 0 0 0 0 -875/3 0 -775/3 350/3 1000/3|4495000]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 1 , 10 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{6} & 0 & 0 & 0 & 0 & \\frac{3}{11} & -\\frac{4}{11} & 0 & -\\frac{2}{11} & \\frac{1}{11} & 1 & \\frac{1500}{11} \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & \\frac{4}{11} & -\\frac{7}{22} & 0 & \\frac{13}{22} & \\frac{5}{11} & 0 & \\frac{20700}{11} \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & -\\frac{2}{11} & -\\frac{13}{22} & 1 & -\\frac{1}{22} & \\frac{3}{11} & 0 & \\frac{8900}{11} \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 400 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & -\\frac{3}{11} & \\frac{4}{11} & 0 & \\frac{2}{11} & -\\frac{1}{11} & 0 & \\frac{4000}{11} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & -\\frac{1000}{11} & -\\frac{1875}{11} & 0 & -\\frac{2175}{11} & \\frac{950}{11} & 0 & \\frac{49945000}{11}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{6} & 0 & 0 & 0 & 0 & \\frac{3}{11} & -\\frac{4}{11} & 0 & -\\frac{2}{11} & \\frac{1}{11} & 1 & \\frac{1500}{11} \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & \\frac{4}{11} & -\\frac{7}{22} & 0 & \\frac{13}{22} & \\frac{5}{11} & 0 & \\frac{20700}{11} \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & -\\frac{2}{11} & -\\frac{13}{22} & 1 & -\\frac{1}{22} & \\frac{3}{11} & 0 & \\frac{8900}{11} \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 400 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & -\\frac{3}{11} & \\frac{4}{11} & 0 & \\frac{2}{11} & -\\frac{1}{11} & 0 & \\frac{4000}{11} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & -\\frac{1000}{11} & -\\frac{1875}{11} & 0 & -\\frac{2175}{11} & \\frac{950}{11} & 0 & \\frac{49945000}{11}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n", "[-----------+-----------------------------------------------------------------------------------------------------------------------+-----------]\n", "[ s6| 0 0 0 0 3/11 -4/11 0 -2/11 1/11 1| 1500/11]\n", "[ x1| 1 0 0 0 4/11 -7/22 0 13/22 5/11 0| 20700/11]\n", "[ s3| 0 0 0 0 -2/11 -13/22 1 -1/22 3/11 0| 8900/11]\n", "[ x2| 0 1 0 0 0 0 0 -1 0 0| 200]\n", "[ x3| 0 0 1 0 0 0 0 0 -1 0| 400]\n", "[ x4| 0 0 0 1 -3/11 4/11 0 2/11 -1/11 0| 4000/11]\n", "[-----------+-----------------------------------------------------------------------------------------------------------------------+-----------]\n", "[ Z| 0 0 0 0 -1000/11 -1875/11 0 -2175/11 950/11 0|49945000/11]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 1 , 9 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{5} & 0 & 0 & 0 & 0 & 3 & -4 & 0 & -2 & 1 & 11 & 1500 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & -1 & \\frac{3}{2} & 0 & \\frac{3}{2} & 0 & -5 & 1200 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & -1 & \\frac{1}{2} & 1 & \\frac{1}{2} & 0 & -3 & 400 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 3 & -4 & 0 & -2 & 0 & 11 & 1900 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & -350 & 175 & 0 & -25 & 0 & -950 & 4670000\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{5} & 0 & 0 & 0 & 0 & 3 & -4 & 0 & -2 & 1 & 11 & 1500 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & -1 & \\frac{3}{2} & 0 & \\frac{3}{2} & 0 & -5 & 1200 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & -1 & \\frac{1}{2} & 1 & \\frac{1}{2} & 0 & -3 & 400 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 3 & -4 & 0 & -2 & 0 & 11 & 1900 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & -350 & 175 & 0 & -25 & 0 & -950 & 4670000\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n", "[-------+-------------------------------------------------------------------------------+-------]\n", "[ s5| 0 0 0 0 3 -4 0 -2 1 11| 1500]\n", "[ x1| 1 0 0 0 -1 3/2 0 3/2 0 -5| 1200]\n", "[ s3| 0 0 0 0 -1 1/2 1 1/2 0 -3| 400]\n", "[ x2| 0 1 0 0 0 0 0 -1 0 0| 200]\n", "[ x3| 0 0 1 0 3 -4 0 -2 0 11| 1900]\n", "[ x4| 0 0 0 1 0 0 0 0 0 1| 500]\n", "[-------+-------------------------------------------------------------------------------+-------]\n", "[ Z| 0 0 0 0 -350 175 0 -25 0 -950|4670000]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 2 , 6 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{5} & \\frac{8}{3} & 0 & 0 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 1 & -\\frac{7}{3} & 4700 \\\\\n", "{\\color{green}{s}}_{2} & \\frac{2}{3} & 0 & 0 & 0 & -\\frac{2}{3} & 1 & 0 & 1 & 0 & -\\frac{10}{3} & 800 \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{1}{3} & 0 & 0 & 0 & -\\frac{2}{3} & 0 & 1 & 0 & 0 & -\\frac{4}{3} & 0 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & \\frac{8}{3} & 0 & 1 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 0 & -\\frac{7}{3} & 5100 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{350}{3} & 0 & 0 & 0 & -\\frac{700}{3} & 0 & 0 & -200 & 0 & -\\frac{1100}{3} & 4810000\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{5} & \\frac{8}{3} & 0 & 0 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 1 & -\\frac{7}{3} & 4700 \\\\\n", "{\\color{green}{s}}_{2} & \\frac{2}{3} & 0 & 0 & 0 & -\\frac{2}{3} & 1 & 0 & 1 & 0 & -\\frac{10}{3} & 800 \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{1}{3} & 0 & 0 & 0 & -\\frac{2}{3} & 0 & 1 & 0 & 0 & -\\frac{4}{3} & 0 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & \\frac{8}{3} & 0 & 1 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 0 & -\\frac{7}{3} & 5100 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{350}{3} & 0 & 0 & 0 & -\\frac{700}{3} & 0 & 0 & -200 & 0 & -\\frac{1100}{3} & 4810000\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n", "[-------+-------------------------------------------------------------------------------+-------]\n", "[ s5| 8/3 0 0 0 1/3 0 0 2 1 -7/3| 4700]\n", "[ s2| 2/3 0 0 0 -2/3 1 0 1 0 -10/3| 800]\n", "[ s3| -1/3 0 0 0 -2/3 0 1 0 0 -4/3| 0]\n", "[ x2| 0 1 0 0 0 0 0 -1 0 0| 200]\n", "[ x3| 8/3 0 1 0 1/3 0 0 2 0 -7/3| 5100]\n", "[ x4| 0 0 0 1 0 0 0 0 0 1| 500]\n", "[-------+-------------------------------------------------------------------------------+-------]\n", "[ Z| -350/3 0 0 0 -700/3 0 0 -200 0 -1100/3|4810000]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "El problema es óptimo\n" ] } ], "source": [ "tipo='max' # max o min\n", "\n", "n=4 # número de variables x's\n", "m=6 # número de restricciones (distintas de las de signo)\n", "\n", "c=matrix(QQ,1,n,[1750,1200,700,2000] ) # vector de costos\n", "\n", "A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n", "[8,6,3,7],\n", "[6,5,2,8],\n", "[5,4,2,6],\n", "[0,1,0,0],\n", "[0,0,1,0],\n", "[0,0,0,1]\n", "])\n", "\n", "b=matrix(QQ,m,1,[20000,16000,14000,200,400,500]) # vector de la derecha\n", "\n", "\n", "######################################################\n", "############### VARIABLES DE HOLGURA ################\n", "\n", "\n", "h=matrix(ZZ,1,m,[1,1,1,-1,-1,1]) # variables de holgura: \n", " # Pon 1 si va sumando, \n", " # -1 si va restando y \n", " # 0 si no hay variable de holgura.\n", "\n", "\n", "\n", "\n", "####################################################################\n", "############ HASTA AQUÍ LOS DATOS ################################\n", "####################################################################\n", "\n", "load('https://sage.unex.es/501708/simplex2023Auto.sage')\n", "#load('https://sage.unex.es/501708/simplex2023AutoREVISED.sage')\n", "#load('https://sage.unex.es/501708/simplex2023CompletamenteManual.sage')\n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "scrolled": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|rr}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} & {b_1} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{5} & \\frac{8}{3} & 0 & 0 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 1 & -\\frac{7}{3} & 4700 & \\frac{1}{3} \\\\\n", "{\\color{green}{s}}_{2} & \\frac{2}{3} & 0 & 0 & 0 & -\\frac{2}{3} & 1 & 0 & 1 & 0 & -\\frac{10}{3} & 800 & -\\frac{2}{3} \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{1}{3} & 0 & 0 & 0 & -\\frac{2}{3} & 0 & 1 & 0 & 0 & -\\frac{4}{3} & 0 & -\\frac{2}{3} \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 & 0 \\\\\n", "{x}_{3} & \\frac{8}{3} & 0 & 1 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 0 & -\\frac{7}{3} & 5100 & \\frac{1}{3} \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 & 0 \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{350}{3} & 0 & 0 & 0 & -\\frac{700}{3} & 0 & 0 & -200 & 0 & -\\frac{1100}{3} & 4810000 & \\frac{700}{3}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|rr}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} & {b_1} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{5} & \\frac{8}{3} & 0 & 0 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 1 & -\\frac{7}{3} & 4700 & \\frac{1}{3} \\\\\n", "{\\color{green}{s}}_{2} & \\frac{2}{3} & 0 & 0 & 0 & -\\frac{2}{3} & 1 & 0 & 1 & 0 & -\\frac{10}{3} & 800 & -\\frac{2}{3} \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{1}{3} & 0 & 0 & 0 & -\\frac{2}{3} & 0 & 1 & 0 & 0 & -\\frac{4}{3} & 0 & -\\frac{2}{3} \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 & 0 \\\\\n", "{x}_{3} & \\frac{8}{3} & 0 & 1 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 0 & -\\frac{7}{3} & 5100 & \\frac{1}{3} \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 & 0 \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{350}{3} & 0 & 0 & 0 & -\\frac{700}{3} & 0 & 0 & -200 & 0 & -\\frac{1100}{3} & 4810000 & \\frac{700}{3}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs rhs1]\n", "[-------+-------------------------------------------------------------------------------+---------------]\n", "[ s5| 8/3 0 0 0 1/3 0 0 2 1 -7/3| 4700 1/3]\n", "[ s2| 2/3 0 0 0 -2/3 1 0 1 0 -10/3| 800 -2/3]\n", "[ s3| -1/3 0 0 0 -2/3 0 1 0 0 -4/3| 0 -2/3]\n", "[ x2| 0 1 0 0 0 0 0 -1 0 0| 200 0]\n", "[ x3| 8/3 0 1 0 1/3 0 0 2 0 -7/3| 5100 1/3]\n", "[ x4| 0 0 0 1 0 0 0 0 0 1| 500 0]\n", "[-------+-------------------------------------------------------------------------------+---------------]\n", "[ Z| -350/3 0 0 0 -700/3 0 0 -200 0 -1100/3|4810000 700/3]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "b1p=matrix(QQ,m,1,[1,0,0,0,0,0]); param1b(b1p) " ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[350.00 NO NO NO 350.00 NO NO NO NO 275.00]" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cocientesD(3)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|rr}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} & {b_1} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{5} & \\frac{13}{4} & 0 & 0 & 0 & \\frac{3}{2} & 0 & -\\frac{7}{4} & 2 & 1 & 0 & 4700 & \\frac{3}{2} \\\\\n", "{\\color{green}{s}}_{2} & \\frac{3}{2} & 0 & 0 & 0 & 1 & 1 & -\\frac{5}{2} & 1 & 0 & 0 & 800 & 1 \\\\\n", "{\\color{green}{s}}_{6} & \\frac{1}{4} & 0 & 0 & 0 & \\frac{1}{2} & 0 & -\\frac{3}{4} & 0 & 0 & 1 & 0 & \\frac{1}{2} \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 & 0 \\\\\n", "{x}_{3} & \\frac{13}{4} & 0 & 1 & 0 & \\frac{3}{2} & 0 & -\\frac{7}{4} & 2 & 0 & 0 & 5100 & \\frac{3}{2} \\\\\n", "{x}_{4} & -\\frac{1}{4} & 0 & 0 & 1 & -\\frac{1}{2} & 0 & \\frac{3}{4} & 0 & 0 & 0 & 500 & -\\frac{1}{2} \\\\\n", "\\hline\n", " {Z_{ind}} & -25 & 0 & 0 & 0 & -50 & 0 & -275 & -200 & 0 & 0 & 4810000 & 50\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|rr}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} & {b_1} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{5} & \\frac{13}{4} & 0 & 0 & 0 & \\frac{3}{2} & 0 & -\\frac{7}{4} & 2 & 1 & 0 & 4700 & \\frac{3}{2} \\\\\n", "{\\color{green}{s}}_{2} & \\frac{3}{2} & 0 & 0 & 0 & 1 & 1 & -\\frac{5}{2} & 1 & 0 & 0 & 800 & 1 \\\\\n", "{\\color{green}{s}}_{6} & \\frac{1}{4} & 0 & 0 & 0 & \\frac{1}{2} & 0 & -\\frac{3}{4} & 0 & 0 & 1 & 0 & \\frac{1}{2} \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 & 0 \\\\\n", "{x}_{3} & \\frac{13}{4} & 0 & 1 & 0 & \\frac{3}{2} & 0 & -\\frac{7}{4} & 2 & 0 & 0 & 5100 & \\frac{3}{2} \\\\\n", "{x}_{4} & -\\frac{1}{4} & 0 & 0 & 1 & -\\frac{1}{2} & 0 & \\frac{3}{4} & 0 & 0 & 0 & 500 & -\\frac{1}{2} \\\\\n", "\\hline\n", " {Z_{ind}} & -25 & 0 & 0 & 0 & -50 & 0 & -275 & -200 & 0 & 0 & 4810000 & 50\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs rhs1]\n", "[-------+-------------------------------------------------------------------------------+---------------]\n", "[ s5| 13/4 0 0 0 3/2 0 -7/4 2 1 0| 4700 3/2]\n", "[ s2| 3/2 0 0 0 1 1 -5/2 1 0 0| 800 1]\n", "[ s6| 1/4 0 0 0 1/2 0 -3/4 0 0 1| 0 1/2]\n", "[ x2| 0 1 0 0 0 0 0 -1 0 0| 200 0]\n", "[ x3| 13/4 0 1 0 3/2 0 -7/4 2 0 0| 5100 3/2]\n", "[ x4| -1/4 0 0 1 -1/2 0 3/4 0 0 0| 500 -1/2]\n", "[-------+-------------------------------------------------------------------------------+---------------]\n", "[ Z| -25 0 0 0 -50 0 -275 -200 0 0|4810000 50]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(3,10)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/usr/lib/python3/dist-packages/sage/misc/remote_file.py:46: DeprecationWarning: ssl.SSLContext() without protocol argument is deprecated.\n", " content = urlopen(req, timeout=1, context=SSLContext())\n", "/usr/lib/python3/dist-packages/sage/misc/remote_file.py:46: DeprecationWarning: ssl.PROTOCOL_TLS is deprecated\n", " content = urlopen(req, timeout=1, context=SSLContext())\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$ " ], "text/latex": [ 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"\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{red}{t}}_{4} & {\\color{red}{t}}_{5} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 8 & 0 & 3 & 7 & 1 & 0 & 0 & 6 & 0 & 0 & -6 & 0 & 18800 \\\\\n", "{\\color{green}{s}}_{2} & 6 & 0 & 2 & 8 & 0 & 1 & 0 & 5 & 0 & 0 & -5 & 0 & 15000 \\\\\n", "{\\color{green}{s}}_{3} & 5 & 0 & 2 & 6 & 0 & 0 & 1 & 4 & 0 & 0 & -4 & 0 & 13200 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 200 \\\\\n", "{\\color{red}{t}}_{5} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 400 \\\\\n", "{\\color{green}{s}}_{6} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 500 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 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{\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{red}{t}}_{4} & {\\color{red}{t}}_{5} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 8 & 0 & 0 & 7 & 1 & 0 & 0 & 6 & 3 & 0 & -6 & -3 & 17600 \\\\\n", "{\\color{green}{s}}_{2} & 6 & 0 & 0 & 8 & 0 & 1 & 0 & 5 & 2 & 0 & -5 & -2 & 14200 \\\\\n", "{\\color{green}{s}}_{3} & 5 & 0 & 0 & 6 & 0 & 0 & 1 & 4 & 2 & 0 & -4 & -2 & 12400 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 400 \\\\\n", "{\\color{green}{s}}_{6} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 500 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{red}{t}}_{4} & {\\color{red}{t}}_{5} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 8 & 0 & 0 & 7 & 1 & 0 & 0 & 6 & 3 & 0 & -6 & -3 & 17600 \\\\\n", "{\\color{green}{s}}_{2} & 6 & 0 & 0 & 8 & 0 & 1 & 0 & 5 & 2 & 0 & -5 & -2 & 14200 \\\\\n", "{\\color{green}{s}}_{3} & 5 & 0 & 0 & 6 & 0 & 0 & 1 & 4 & 2 & 0 & -4 & -2 & 12400 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 400 \\\\\n", "{\\color{green}{s}}_{6} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 500 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 t4 t5| rhs]\n", "[-----+-----------------------------------------------------------------------+-----]\n", "[ s1| 8 0 0 7 1 0 0 6 3 0 -6 -3|17600]\n", "[ s2| 6 0 0 8 0 1 0 5 2 0 -5 -2|14200]\n", "[ s3| 5 0 0 6 0 0 1 4 2 0 -4 -2|12400]\n", "[ x2| 0 1 0 0 0 0 0 -1 0 0 1 0| 200]\n", "[ x3| 0 0 1 0 0 0 0 0 -1 0 0 1| 400]\n", "[ s6| 0 0 0 1 0 0 0 0 0 1 0 0| 500]\n", "[-----+-----------------------------------------------------------------------+-----]\n", "[ W| 0 0 0 0 0 0 0 0 0 0 1 1| 0]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "El problema de la fase I es óptimo y Wopt=0. Por tanto, el original es factible\n", "Preparemos el cuadro inicial de la fase II\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\ \\ \\ Fase\\ II}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\ \\ \\ Fase\\ II}$$" ], "text/plain": [ "FII" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " 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8 0 1 0 5 2 0| 14200]\n", "[ s3| 5 0 0 6 0 0 1 4 2 0| 12400]\n", "[ x2| 0 1 0 0 0 0 0 -1 0 0| 200]\n", "[ x3| 0 0 1 0 0 0 0 0 -1 0| 400]\n", "[ s6| 0 0 0 1 0 0 0 0 0 1| 500]\n", "[------+---------------------------------------------------------------------+------]\n", "[ Z| 1750 0 0 2000 0 0 0 1200 700 0|520000]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 6 , 4 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 8 & 0 & 0 & 0 & 1 & 0 & 0 & 6 & 3 & -7 & 14100 \\\\\n", "{\\color{green}{s}}_{2} & 6 & 0 & 0 & 0 & 0 & 1 & 0 & 5 & 2 & -8 & 10200 \\\\\n", "{\\color{green}{s}}_{3} & 5 & 0 & 0 & 0 & 0 & 0 & 1 & 4 & 2 & -6 & 9400 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 400 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n", "\\hline\n", " {Z_{ind}} & 1750 & 0 & 0 & 0 & 0 & 0 & 0 & 1200 & 700 & -2000 & 1520000\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 8 & 0 & 0 & 0 & 1 & 0 & 0 & 6 & 3 & -7 & 14100 \\\\\n", "{\\color{green}{s}}_{2} & 6 & 0 & 0 & 0 & 0 & 1 & 0 & 5 & 2 & -8 & 10200 \\\\\n", "{\\color{green}{s}}_{3} & 5 & 0 & 0 & 0 & 0 & 0 & 1 & 4 & 2 & -6 & 9400 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 400 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n", "\\hline\n", " {Z_{ind}} & 1750 & 0 & 0 & 0 & 0 & 0 & 0 & 1200 & 700 & -2000 & 1520000\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n", "[-------+-------------------------------------------------------------------------------+-------]\n", "[ s1| 8 0 0 0 1 0 0 6 3 -7| 14100]\n", "[ s2| 6 0 0 0 0 1 0 5 2 -8| 10200]\n", "[ s3| 5 0 0 0 0 0 1 4 2 -6| 9400]\n", "[ x2| 0 1 0 0 0 0 0 -1 0 0| 200]\n", "[ x3| 0 0 1 0 0 0 0 0 -1 0| 400]\n", "[ x4| 0 0 0 1 0 0 0 0 0 1| 500]\n", "[-------+-------------------------------------------------------------------------------+-------]\n", "[ Z| 1750 0 0 0 0 0 0 1200 700 -2000|1520000]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 2 , 1 )\n" ] }, { "data": { "text/html": [ " 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4495000\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 0 & 0 & 0 & 1 & -\\frac{4}{3} & 0 & -\\frac{2}{3} & \\frac{1}{3} & \\frac{11}{3} & 500 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & \\frac{1}{6} & 0 & \\frac{5}{6} & \\frac{1}{3} & -\\frac{4}{3} & 1700 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & 0 & -\\frac{5}{6} & 1 & -\\frac{1}{6} & \\frac{1}{3} & \\frac{2}{3} & 900 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 400 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & 0 & -\\frac{875}{3} & 0 & -\\frac{775}{3} & \\frac{350}{3} & \\frac{1000}{3} & 4495000\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n", "[-------+-------------------------------------------------------------------------------+-------]\n", "[ s1| 0 0 0 0 1 -4/3 0 -2/3 1/3 11/3| 500]\n", "[ x1| 1 0 0 0 0 1/6 0 5/6 1/3 -4/3| 1700]\n", "[ s3| 0 0 0 0 0 -5/6 1 -1/6 1/3 2/3| 900]\n", "[ x2| 0 1 0 0 0 0 0 -1 0 0| 200]\n", "[ x3| 0 0 1 0 0 0 0 0 -1 0| 400]\n", "[ x4| 0 0 0 1 0 0 0 0 0 1| 500]\n", "[-------+-------------------------------------------------------------------------------+-------]\n", "[ Z| 0 0 0 0 0 -875/3 0 -775/3 350/3 1000/3|4495000]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 1 , 10 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & 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"\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{6} & 0 & 0 & 0 & 0 & \\frac{3}{11} & -\\frac{4}{11} & 0 & -\\frac{2}{11} & \\frac{1}{11} & 1 & \\frac{1500}{11} \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & \\frac{4}{11} & -\\frac{7}{22} & 0 & \\frac{13}{22} & \\frac{5}{11} & 0 & \\frac{20700}{11} \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & -\\frac{2}{11} & -\\frac{13}{22} & 1 & -\\frac{1}{22} & \\frac{3}{11} & 0 & \\frac{8900}{11} \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 400 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & -\\frac{3}{11} & \\frac{4}{11} & 0 & \\frac{2}{11} & -\\frac{1}{11} 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"name": "stdout", "output_type": "stream", "text": [ "cambio( 1 , 9 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{5} & 0 & 0 & 0 & 0 & 3 & -4 & 0 & -2 & 1 & 11 & 1500 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & -1 & \\frac{3}{2} & 0 & \\frac{3}{2} & 0 & -5 & 1200 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & -1 & \\frac{1}{2} & 1 & \\frac{1}{2} & 0 & -3 & 400 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 3 & -4 & 0 & -2 & 0 & 11 & 1900 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & -350 & 175 & 0 & -25 & 0 & -950 & 4670000\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{5} & 0 & 0 & 0 & 0 & 3 & -4 & 0 & -2 & 1 & 11 & 1500 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & -1 & \\frac{3}{2} & 0 & \\frac{3}{2} & 0 & -5 & 1200 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & -1 & \\frac{1}{2} & 1 & \\frac{1}{2} & 0 & -3 & 400 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 3 & -4 & 0 & -2 & 0 & 11 & 1900 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & -350 & 175 & 0 & -25 & 0 & -950 & 4670000\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n", "[-------+-------------------------------------------------------------------------------+-------]\n", "[ s5| 0 0 0 0 3 -4 0 -2 1 11| 1500]\n", "[ x1| 1 0 0 0 -1 3/2 0 3/2 0 -5| 1200]\n", "[ s3| 0 0 0 0 -1 1/2 1 1/2 0 -3| 400]\n", "[ x2| 0 1 0 0 0 0 0 -1 0 0| 200]\n", "[ x3| 0 0 1 0 3 -4 0 -2 0 11| 1900]\n", "[ x4| 0 0 0 1 0 0 0 0 0 1| 500]\n", "[-------+-------------------------------------------------------------------------------+-------]\n", "[ Z| 0 0 0 0 -350 175 0 -25 0 -950|4670000]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 2 , 6 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{5} & \\frac{8}{3} & 0 & 0 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 1 & -\\frac{7}{3} & 4700 \\\\\n", "{\\color{green}{s}}_{2} & \\frac{2}{3} & 0 & 0 & 0 & -\\frac{2}{3} & 1 & 0 & 1 & 0 & -\\frac{10}{3} & 800 \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{1}{3} & 0 & 0 & 0 & -\\frac{2}{3} & 0 & 1 & 0 & 0 & -\\frac{4}{3} & 0 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & \\frac{8}{3} & 0 & 1 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 0 & -\\frac{7}{3} & 5100 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{350}{3} & 0 & 0 & 0 & -\\frac{700}{3} & 0 & 0 & -200 & 0 & -\\frac{1100}{3} & 4810000\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{5} & \\frac{8}{3} & 0 & 0 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 1 & -\\frac{7}{3} & 4700 \\\\\n", "{\\color{green}{s}}_{2} & \\frac{2}{3} & 0 & 0 & 0 & -\\frac{2}{3} & 1 & 0 & 1 & 0 & -\\frac{10}{3} & 800 \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{1}{3} & 0 & 0 & 0 & -\\frac{2}{3} & 0 & 1 & 0 & 0 & -\\frac{4}{3} & 0 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & \\frac{8}{3} & 0 & 1 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 0 & -\\frac{7}{3} & 5100 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{350}{3} & 0 & 0 & 0 & -\\frac{700}{3} & 0 & 0 & -200 & 0 & -\\frac{1100}{3} & 4810000\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n", "[-------+-------------------------------------------------------------------------------+-------]\n", "[ s5| 8/3 0 0 0 1/3 0 0 2 1 -7/3| 4700]\n", "[ s2| 2/3 0 0 0 -2/3 1 0 1 0 -10/3| 800]\n", "[ s3| -1/3 0 0 0 -2/3 0 1 0 0 -4/3| 0]\n", "[ x2| 0 1 0 0 0 0 0 -1 0 0| 200]\n", "[ x3| 8/3 0 1 0 1/3 0 0 2 0 -7/3| 5100]\n", "[ x4| 0 0 0 1 0 0 0 0 0 1| 500]\n", "[-------+-------------------------------------------------------------------------------+-------]\n", "[ Z| -350/3 0 0 0 -700/3 0 0 -200 0 -1100/3|4810000]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "El problema es óptimo\n" ] } ], "source": [ "tipo='max' # max o min\n", "\n", "n=4 # número de variables x's\n", "m=6 # número de restricciones (distintas de las de signo)\n", "\n", "c=matrix(QQ,1,n,[1750,1200,700,2000] ) # vector de costos\n", "\n", "A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n", "[8,6,3,7],\n", "[6,5,2,8],\n", "[5,4,2,6],\n", "[0,1,0,0],\n", "[0,0,1,0],\n", "[0,0,0,1]\n", "])\n", "\n", "b=matrix(QQ,m,1,[20000,16000,14000,200,400,500]) # vector de la derecha\n", "\n", "\n", "######################################################\n", "############### VARIABLES DE HOLGURA ################\n", "\n", "\n", "h=matrix(ZZ,1,m,[1,1,1,-1,-1,1]) # variables de holgura: \n", " # Pon 1 si va sumando, \n", " # -1 si va restando y \n", " # 0 si no hay variable de holgura.\n", "\n", "\n", "\n", "\n", "####################################################################\n", "############ HASTA AQUÍ LOS DATOS ################################\n", "####################################################################\n", "\n", "load('https://sage.unex.es/501708/simplex2023Auto.sage')\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|rr}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} & {b_1} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{5} & \\frac{8}{3} & 0 & 0 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 1 & -\\frac{7}{3} & 4700 & 0 \\\\\n", "{\\color{green}{s}}_{2} & \\frac{2}{3} & 0 & 0 & 0 & -\\frac{2}{3} & 1 & 0 & 1 & 0 & -\\frac{10}{3} & 800 & 1 \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{1}{3} & 0 & 0 & 0 & -\\frac{2}{3} & 0 & 1 & 0 & 0 & -\\frac{4}{3} & 0 & 0 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 & 0 \\\\\n", "{x}_{3} & \\frac{8}{3} & 0 & 1 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 0 & -\\frac{7}{3} & 5100 & 0 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 & 0 \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{350}{3} & 0 & 0 & 0 & -\\frac{700}{3} & 0 & 0 & -200 & 0 & -\\frac{1100}{3} & 4810000 & 0\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|rr}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} & {b_1} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{5} & \\frac{8}{3} & 0 & 0 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 1 & -\\frac{7}{3} & 4700 & 0 \\\\\n", "{\\color{green}{s}}_{2} & \\frac{2}{3} & 0 & 0 & 0 & -\\frac{2}{3} & 1 & 0 & 1 & 0 & -\\frac{10}{3} & 800 & 1 \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{1}{3} & 0 & 0 & 0 & -\\frac{2}{3} & 0 & 1 & 0 & 0 & -\\frac{4}{3} & 0 & 0 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 & 0 \\\\\n", "{x}_{3} & \\frac{8}{3} & 0 & 1 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 0 & -\\frac{7}{3} & 5100 & 0 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 & 0 \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{350}{3} & 0 & 0 & 0 & -\\frac{700}{3} & 0 & 0 & -200 & 0 & -\\frac{1100}{3} & 4810000 & 0\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs rhs1]\n", "[-------+-------------------------------------------------------------------------------+---------------]\n", "[ s5| 8/3 0 0 0 1/3 0 0 2 1 -7/3| 4700 0]\n", "[ s2| 2/3 0 0 0 -2/3 1 0 1 0 -10/3| 800 1]\n", "[ s3| -1/3 0 0 0 -2/3 0 1 0 0 -4/3| 0 0]\n", "[ x2| 0 1 0 0 0 0 0 -1 0 0| 200 0]\n", "[ x3| 8/3 0 1 0 1/3 0 0 2 0 -7/3| 5100 0]\n", "[ x4| 0 0 0 1 0 0 0 0 0 1| 500 0]\n", "[-------+-------------------------------------------------------------------------------+---------------]\n", "[ Z| -350/3 0 0 0 -700/3 0 0 -200 0 -1100/3|4810000 0]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "b1p=matrix(QQ,m,1,[0,1,0,0,0,0]); param1b(b1p) " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n", "\\begin{array}{lcrcrcrcrcl}\n", " \\max \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 1750 x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 1200 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 700 x_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2000 x_{4} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 8 x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 6 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 3 x_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 7 x_{4} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 20000 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 6 x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 5 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 8 x_{4} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 16000 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 5 x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 4 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 6 x_{4} \\mspace{-6mu}&\\mspace{-6mu} \\leq 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\\mspace{-6mu}&\\mspace{-6mu} 500 \\\\\n", "\\end{array} \\\\\n", "x_{1}, x_{2}, x_{3}, x_{4} \\geq 0\n", "\\end{array}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n", "\\begin{array}{lcrcrcrcrcl}\n", " \\max \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 1750 x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 1200 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 700 x_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2000 x_{4} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 8 x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 6 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 3 x_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 7 x_{4} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 20000 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 6 x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 5 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 8 x_{4} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 16000 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 5 x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 4 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 6 x_{4} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 14000 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} x_{2} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 200 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} x_{3} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 400 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} x_{4} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 500 \\\\\n", "\\end{array} \\\\\n", "x_{1}, x_{2}, x_{3}, x_{4} \\geq 0\n", "\\end{array}$$" ], "text/plain": [ "LP problem (use 'view(...)' or '%display typeset' for details)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}4810000$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}4810000$$" ], "text/plain": [ "4810000" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(0,\\,200,\\,5100,\\,500\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(0,\\,200,\\,5100,\\,500\\right)$$" ], "text/plain": [ "(0, 200, 5100, 500)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{}$$" ], "text/plain": [ "salto" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\texttt{El dual es:}}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\texttt{El dual es:}}$$" ], "text/plain": [ "dual" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n", "\\begin{array}{lcrcrcrcrcrcrcl}\n", " \\min \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 20000 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400 y_{5} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 500 y_{6} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 8 y_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 6 y_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 5 y_{3} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 1750 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 6 y_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 5 y_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 4 y_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{4} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 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\\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 2000 \\\\\n", "\\end{array} \\\\\n", "y_{1} \\geq 0,\\ y_{2} \\geq 0,\\ y_{3} \\geq 0,\\ y_{4} \\leq 0,\\ y_{5} \\leq 0,\\ y_{6} \\geq 0\n", "\\end{array}$$" ], "text/plain": [ "LP problem (use 'view(...)' or '%display typeset' for details)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}4810000$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}4810000$$" ], "text/plain": [ "4810000" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(50,\\,0,\\,275,\\,-200,\\,0,\\,0\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(50,\\,0,\\,275,\\,-200,\\,0,\\,0\\right)$$" ], "text/plain": [ "(50, 0, 275, -200, 0, 0)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{}$$" ], "text/plain": [ "salto" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\ \\ \\ Fase\\ I}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\ \\ \\ Fase\\ I}$$" ], "text/plain": [ "FI" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{red}{t}}_{4} & {\\color{red}{t}}_{5} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 8 & 6 & 3 & 7 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 20000 \\\\\n", "{\\color{green}{s}}_{2} & 6 & 5 & 2 & 8 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 16000 \\\\\n", "{\\color{green}{s}}_{3} & 5 & 4 & 2 & 6 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 14000 \\\\\n", "{\\color{red}{t}}_{4} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 200 \\\\\n", "{\\color{red}{t}}_{5} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 400 \\\\\n", "{\\color{green}{s}}_{6} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 500 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & -1 & -1 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 600\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{red}{t}}_{4} & {\\color{red}{t}}_{5} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 8 & 6 & 3 & 7 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 20000 \\\\\n", "{\\color{green}{s}}_{2} & 6 & 5 & 2 & 8 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 16000 \\\\\n", "{\\color{green}{s}}_{3} & 5 & 4 & 2 & 6 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 14000 \\\\\n", "{\\color{red}{t}}_{4} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 200 \\\\\n", "{\\color{red}{t}}_{5} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 400 \\\\\n", "{\\color{green}{s}}_{6} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 500 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & -1 & -1 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 600\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 t4 t5| rhs]\n", "[-----+-----------------------------------------------------------------------+-----]\n", "[ s1| 8 6 3 7 1 0 0 0 0 0 0 0|20000]\n", "[ s2| 6 5 2 8 0 1 0 0 0 0 0 0|16000]\n", "[ s3| 5 4 2 6 0 0 1 0 0 0 0 0|14000]\n", "[ t4| 0 1 0 0 0 0 0 -1 0 0 1 0| 200]\n", "[ t5| 0 0 1 0 0 0 0 0 -1 0 0 1| 400]\n", "[ s6| 0 0 0 1 0 0 0 0 0 1 0 0| 500]\n", "[-----+-----------------------------------------------------------------------+-----]\n", "[ W| 0 -1 -1 0 0 0 0 1 1 0 0 0| 600]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 4 , 2 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{red}{t}}_{4} & {\\color{red}{t}}_{5} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 8 & 0 & 3 & 7 & 1 & 0 & 0 & 6 & 0 & 0 & -6 & 0 & 18800 \\\\\n", "{\\color{green}{s}}_{2} & 6 & 0 & 2 & 8 & 0 & 1 & 0 & 5 & 0 & 0 & -5 & 0 & 15000 \\\\\n", "{\\color{green}{s}}_{3} & 5 & 0 & 2 & 6 & 0 & 0 & 1 & 4 & 0 & 0 & -4 & 0 & 13200 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 200 \\\\\n", "{\\color{red}{t}}_{5} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 400 \\\\\n", "{\\color{green}{s}}_{6} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 500 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 400\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{red}{t}}_{4} & {\\color{red}{t}}_{5} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 8 & 0 & 3 & 7 & 1 & 0 & 0 & 6 & 0 & 0 & -6 & 0 & 18800 \\\\\n", "{\\color{green}{s}}_{2} & 6 & 0 & 2 & 8 & 0 & 1 & 0 & 5 & 0 & 0 & -5 & 0 & 15000 \\\\\n", "{\\color{green}{s}}_{3} & 5 & 0 & 2 & 6 & 0 & 0 & 1 & 4 & 0 & 0 & -4 & 0 & 13200 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 200 \\\\\n", "{\\color{red}{t}}_{5} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 400 \\\\\n", "{\\color{green}{s}}_{6} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 500 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 400\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 t4 t5| rhs]\n", "[-----+-----------------------------------------------------------------------+-----]\n", "[ s1| 8 0 3 7 1 0 0 6 0 0 -6 0|18800]\n", "[ s2| 6 0 2 8 0 1 0 5 0 0 -5 0|15000]\n", "[ s3| 5 0 2 6 0 0 1 4 0 0 -4 0|13200]\n", "[ x2| 0 1 0 0 0 0 0 -1 0 0 1 0| 200]\n", "[ t5| 0 0 1 0 0 0 0 0 -1 0 0 1| 400]\n", "[ s6| 0 0 0 1 0 0 0 0 0 1 0 0| 500]\n", "[-----+-----------------------------------------------------------------------+-----]\n", "[ W| 0 0 -1 0 0 0 0 0 1 0 1 0| 400]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 5 , 3 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{red}{t}}_{4} & {\\color{red}{t}}_{5} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 8 & 0 & 0 & 7 & 1 & 0 & 0 & 6 & 3 & 0 & -6 & -3 & 17600 \\\\\n", "{\\color{green}{s}}_{2} & 6 & 0 & 0 & 8 & 0 & 1 & 0 & 5 & 2 & 0 & -5 & -2 & 14200 \\\\\n", "{\\color{green}{s}}_{3} & 5 & 0 & 0 & 6 & 0 & 0 & 1 & 4 & 2 & 0 & -4 & -2 & 12400 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 400 \\\\\n", "{\\color{green}{s}}_{6} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 500 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{red}{t}}_{4} & {\\color{red}{t}}_{5} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 8 & 0 & 0 & 7 & 1 & 0 & 0 & 6 & 3 & 0 & -6 & -3 & 17600 \\\\\n", "{\\color{green}{s}}_{2} & 6 & 0 & 0 & 8 & 0 & 1 & 0 & 5 & 2 & 0 & -5 & -2 & 14200 \\\\\n", "{\\color{green}{s}}_{3} & 5 & 0 & 0 & 6 & 0 & 0 & 1 & 4 & 2 & 0 & -4 & -2 & 12400 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 400 \\\\\n", "{\\color{green}{s}}_{6} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 500 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 t4 t5| rhs]\n", "[-----+-----------------------------------------------------------------------+-----]\n", "[ s1| 8 0 0 7 1 0 0 6 3 0 -6 -3|17600]\n", "[ s2| 6 0 0 8 0 1 0 5 2 0 -5 -2|14200]\n", "[ s3| 5 0 0 6 0 0 1 4 2 0 -4 -2|12400]\n", "[ x2| 0 1 0 0 0 0 0 -1 0 0 1 0| 200]\n", "[ x3| 0 0 1 0 0 0 0 0 -1 0 0 1| 400]\n", "[ s6| 0 0 0 1 0 0 0 0 0 1 0 0| 500]\n", "[-----+-----------------------------------------------------------------------+-----]\n", "[ W| 0 0 0 0 0 0 0 0 0 0 1 1| 0]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "El problema de la fase I es óptimo y Wopt=0. Por tanto, el original es factible\n", "Preparemos el cuadro inicial de la fase II\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\ \\ \\ Fase\\ II}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\ \\ \\ Fase\\ II}$$" ], "text/plain": [ "FII" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 8 & 0 & 0 & 7 & 1 & 0 & 0 & 6 & 3 & 0 & 17600 \\\\\n", "{\\color{green}{s}}_{2} & 6 & 0 & 0 & 8 & 0 & 1 & 0 & 5 & 2 & 0 & 14200 \\\\\n", "{\\color{green}{s}}_{3} & 5 & 0 & 0 & 6 & 0 & 0 & 1 & 4 & 2 & 0 & 12400 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 400 \\\\\n", "{\\color{green}{s}}_{6} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n", "\\hline\n", " {Z_{ind}} & 1750 & 0 & 0 & 2000 & 0 & 0 & 0 & 1200 & 700 & 0 & 520000\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 8 & 0 & 0 & 7 & 1 & 0 & 0 & 6 & 3 & 0 & 17600 \\\\\n", "{\\color{green}{s}}_{2} & 6 & 0 & 0 & 8 & 0 & 1 & 0 & 5 & 2 & 0 & 14200 \\\\\n", "{\\color{green}{s}}_{3} & 5 & 0 & 0 & 6 & 0 & 0 & 1 & 4 & 2 & 0 & 12400 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 400 \\\\\n", "{\\color{green}{s}}_{6} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n", "\\hline\n", " {Z_{ind}} & 1750 & 0 & 0 & 2000 & 0 & 0 & 0 & 1200 & 700 & 0 & 520000\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n", "[------+---------------------------------------------------------------------+------]\n", "[ s1| 8 0 0 7 1 0 0 6 3 0| 17600]\n", "[ s2| 6 0 0 8 0 1 0 5 2 0| 14200]\n", "[ s3| 5 0 0 6 0 0 1 4 2 0| 12400]\n", "[ x2| 0 1 0 0 0 0 0 -1 0 0| 200]\n", "[ x3| 0 0 1 0 0 0 0 0 -1 0| 400]\n", "[ s6| 0 0 0 1 0 0 0 0 0 1| 500]\n", "[------+---------------------------------------------------------------------+------]\n", "[ Z| 1750 0 0 2000 0 0 0 1200 700 0|520000]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 6 , 4 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 8 & 0 & 0 & 0 & 1 & 0 & 0 & 6 & 3 & -7 & 14100 \\\\\n", "{\\color{green}{s}}_{2} & 6 & 0 & 0 & 0 & 0 & 1 & 0 & 5 & 2 & -8 & 10200 \\\\\n", "{\\color{green}{s}}_{3} & 5 & 0 & 0 & 0 & 0 & 0 & 1 & 4 & 2 & -6 & 9400 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 400 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n", "\\hline\n", " {Z_{ind}} & 1750 & 0 & 0 & 0 & 0 & 0 & 0 & 1200 & 700 & -2000 & 1520000\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 8 & 0 & 0 & 0 & 1 & 0 & 0 & 6 & 3 & -7 & 14100 \\\\\n", "{\\color{green}{s}}_{2} & 6 & 0 & 0 & 0 & 0 & 1 & 0 & 5 & 2 & -8 & 10200 \\\\\n", "{\\color{green}{s}}_{3} & 5 & 0 & 0 & 0 & 0 & 0 & 1 & 4 & 2 & -6 & 9400 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 400 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n", "\\hline\n", " {Z_{ind}} & 1750 & 0 & 0 & 0 & 0 & 0 & 0 & 1200 & 700 & -2000 & 1520000\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n", "[-------+-------------------------------------------------------------------------------+-------]\n", "[ s1| 8 0 0 0 1 0 0 6 3 -7| 14100]\n", "[ s2| 6 0 0 0 0 1 0 5 2 -8| 10200]\n", "[ s3| 5 0 0 0 0 0 1 4 2 -6| 9400]\n", "[ x2| 0 1 0 0 0 0 0 -1 0 0| 200]\n", "[ x3| 0 0 1 0 0 0 0 0 -1 0| 400]\n", "[ x4| 0 0 0 1 0 0 0 0 0 1| 500]\n", "[-------+-------------------------------------------------------------------------------+-------]\n", "[ Z| 1750 0 0 0 0 0 0 1200 700 -2000|1520000]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 2 , 1 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 0 & 0 & 0 & 1 & -\\frac{4}{3} & 0 & -\\frac{2}{3} & \\frac{1}{3} & \\frac{11}{3} & 500 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & \\frac{1}{6} & 0 & \\frac{5}{6} & \\frac{1}{3} & -\\frac{4}{3} & 1700 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & 0 & -\\frac{5}{6} & 1 & -\\frac{1}{6} & \\frac{1}{3} & \\frac{2}{3} & 900 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 400 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & 0 & -\\frac{875}{3} & 0 & -\\frac{775}{3} & \\frac{350}{3} & \\frac{1000}{3} & 4495000\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 0 & 0 & 0 & 1 & -\\frac{4}{3} & 0 & -\\frac{2}{3} & \\frac{1}{3} & \\frac{11}{3} & 500 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & \\frac{1}{6} & 0 & \\frac{5}{6} & \\frac{1}{3} & -\\frac{4}{3} & 1700 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & 0 & -\\frac{5}{6} & 1 & -\\frac{1}{6} & \\frac{1}{3} & \\frac{2}{3} & 900 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 400 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & 0 & -\\frac{875}{3} & 0 & -\\frac{775}{3} & \\frac{350}{3} & \\frac{1000}{3} & 4495000\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n", "[-------+-------------------------------------------------------------------------------+-------]\n", "[ s1| 0 0 0 0 1 -4/3 0 -2/3 1/3 11/3| 500]\n", "[ x1| 1 0 0 0 0 1/6 0 5/6 1/3 -4/3| 1700]\n", "[ s3| 0 0 0 0 0 -5/6 1 -1/6 1/3 2/3| 900]\n", "[ x2| 0 1 0 0 0 0 0 -1 0 0| 200]\n", "[ x3| 0 0 1 0 0 0 0 0 -1 0| 400]\n", "[ x4| 0 0 0 1 0 0 0 0 0 1| 500]\n", "[-------+-------------------------------------------------------------------------------+-------]\n", "[ Z| 0 0 0 0 0 -875/3 0 -775/3 350/3 1000/3|4495000]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 1 , 10 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{6} & 0 & 0 & 0 & 0 & \\frac{3}{11} & -\\frac{4}{11} & 0 & -\\frac{2}{11} & \\frac{1}{11} & 1 & \\frac{1500}{11} \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & \\frac{4}{11} & -\\frac{7}{22} & 0 & \\frac{13}{22} & \\frac{5}{11} & 0 & \\frac{20700}{11} \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & -\\frac{2}{11} & -\\frac{13}{22} & 1 & -\\frac{1}{22} & \\frac{3}{11} & 0 & \\frac{8900}{11} \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 400 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & -\\frac{3}{11} & \\frac{4}{11} & 0 & \\frac{2}{11} & -\\frac{1}{11} & 0 & \\frac{4000}{11} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & -\\frac{1000}{11} & -\\frac{1875}{11} & 0 & -\\frac{2175}{11} & \\frac{950}{11} & 0 & \\frac{49945000}{11}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{6} & 0 & 0 & 0 & 0 & \\frac{3}{11} & -\\frac{4}{11} & 0 & -\\frac{2}{11} & \\frac{1}{11} & 1 & \\frac{1500}{11} \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & \\frac{4}{11} & -\\frac{7}{22} & 0 & \\frac{13}{22} & \\frac{5}{11} & 0 & \\frac{20700}{11} \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & -\\frac{2}{11} & -\\frac{13}{22} & 1 & -\\frac{1}{22} & \\frac{3}{11} & 0 & \\frac{8900}{11} \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 400 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & -\\frac{3}{11} & \\frac{4}{11} & 0 & \\frac{2}{11} & -\\frac{1}{11} & 0 & \\frac{4000}{11} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & -\\frac{1000}{11} & -\\frac{1875}{11} & 0 & -\\frac{2175}{11} & \\frac{950}{11} & 0 & \\frac{49945000}{11}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n", "[-----------+-----------------------------------------------------------------------------------------------------------------------+-----------]\n", "[ s6| 0 0 0 0 3/11 -4/11 0 -2/11 1/11 1| 1500/11]\n", "[ x1| 1 0 0 0 4/11 -7/22 0 13/22 5/11 0| 20700/11]\n", "[ s3| 0 0 0 0 -2/11 -13/22 1 -1/22 3/11 0| 8900/11]\n", "[ x2| 0 1 0 0 0 0 0 -1 0 0| 200]\n", "[ x3| 0 0 1 0 0 0 0 0 -1 0| 400]\n", "[ x4| 0 0 0 1 -3/11 4/11 0 2/11 -1/11 0| 4000/11]\n", "[-----------+-----------------------------------------------------------------------------------------------------------------------+-----------]\n", "[ Z| 0 0 0 0 -1000/11 -1875/11 0 -2175/11 950/11 0|49945000/11]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 1 , 9 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{5} & 0 & 0 & 0 & 0 & 3 & -4 & 0 & -2 & 1 & 11 & 1500 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & -1 & \\frac{3}{2} & 0 & \\frac{3}{2} & 0 & -5 & 1200 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & -1 & \\frac{1}{2} & 1 & \\frac{1}{2} & 0 & -3 & 400 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 3 & -4 & 0 & -2 & 0 & 11 & 1900 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & -350 & 175 & 0 & -25 & 0 & -950 & 4670000\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{5} & 0 & 0 & 0 & 0 & 3 & -4 & 0 & -2 & 1 & 11 & 1500 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & -1 & \\frac{3}{2} & 0 & \\frac{3}{2} & 0 & -5 & 1200 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & -1 & \\frac{1}{2} & 1 & \\frac{1}{2} & 0 & -3 & 400 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 3 & -4 & 0 & -2 & 0 & 11 & 1900 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & -350 & 175 & 0 & -25 & 0 & -950 & 4670000\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n", "[-------+-------------------------------------------------------------------------------+-------]\n", "[ s5| 0 0 0 0 3 -4 0 -2 1 11| 1500]\n", "[ x1| 1 0 0 0 -1 3/2 0 3/2 0 -5| 1200]\n", "[ s3| 0 0 0 0 -1 1/2 1 1/2 0 -3| 400]\n", "[ x2| 0 1 0 0 0 0 0 -1 0 0| 200]\n", "[ x3| 0 0 1 0 3 -4 0 -2 0 11| 1900]\n", "[ x4| 0 0 0 1 0 0 0 0 0 1| 500]\n", "[-------+-------------------------------------------------------------------------------+-------]\n", "[ Z| 0 0 0 0 -350 175 0 -25 0 -950|4670000]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 2 , 6 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{5} & \\frac{8}{3} & 0 & 0 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 1 & -\\frac{7}{3} & 4700 \\\\\n", "{\\color{green}{s}}_{2} & \\frac{2}{3} & 0 & 0 & 0 & -\\frac{2}{3} & 1 & 0 & 1 & 0 & -\\frac{10}{3} & 800 \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{1}{3} & 0 & 0 & 0 & -\\frac{2}{3} & 0 & 1 & 0 & 0 & -\\frac{4}{3} & 0 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & \\frac{8}{3} & 0 & 1 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 0 & -\\frac{7}{3} & 5100 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{350}{3} & 0 & 0 & 0 & -\\frac{700}{3} & 0 & 0 & -200 & 0 & -\\frac{1100}{3} & 4810000\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{5} & \\frac{8}{3} & 0 & 0 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 1 & -\\frac{7}{3} & 4700 \\\\\n", "{\\color{green}{s}}_{2} & \\frac{2}{3} & 0 & 0 & 0 & -\\frac{2}{3} & 1 & 0 & 1 & 0 & -\\frac{10}{3} & 800 \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{1}{3} & 0 & 0 & 0 & -\\frac{2}{3} & 0 & 1 & 0 & 0 & -\\frac{4}{3} & 0 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & \\frac{8}{3} & 0 & 1 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 0 & -\\frac{7}{3} & 5100 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{350}{3} & 0 & 0 & 0 & -\\frac{700}{3} & 0 & 0 & -200 & 0 & -\\frac{1100}{3} & 4810000\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n", "[-------+-------------------------------------------------------------------------------+-------]\n", "[ s5| 8/3 0 0 0 1/3 0 0 2 1 -7/3| 4700]\n", "[ s2| 2/3 0 0 0 -2/3 1 0 1 0 -10/3| 800]\n", "[ s3| -1/3 0 0 0 -2/3 0 1 0 0 -4/3| 0]\n", "[ x2| 0 1 0 0 0 0 0 -1 0 0| 200]\n", "[ x3| 8/3 0 1 0 1/3 0 0 2 0 -7/3| 5100]\n", "[ x4| 0 0 0 1 0 0 0 0 0 1| 500]\n", "[-------+-------------------------------------------------------------------------------+-------]\n", "[ Z| -350/3 0 0 0 -700/3 0 0 -200 0 -1100/3|4810000]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "El problema es óptimo\n" ] } ], "source": [ "tipo='max' # max o min\n", "\n", "n=4 # número de variables x's\n", "m=6 # número de restricciones (distintas de las de signo)\n", "\n", "c=matrix(QQ,1,n,[1750,1200,700,2000] ) # vector de costos\n", "\n", "A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n", "[8,6,3,7],\n", "[6,5,2,8],\n", "[5,4,2,6],\n", "[0,1,0,0],\n", "[0,0,1,0],\n", "[0,0,0,1]\n", "])\n", "\n", "b=matrix(QQ,m,1,[20000,16000,14000,200,400,500]) # vector de la derecha\n", "\n", "\n", "######################################################\n", "############### VARIABLES DE HOLGURA ################\n", "\n", "\n", "h=matrix(ZZ,1,m,[1,1,1,-1,-1,1]) # variables de holgura: \n", " # Pon 1 si va sumando, \n", " # -1 si va restando y \n", " # 0 si no hay variable de holgura.\n", "\n", "\n", "\n", "\n", "####################################################################\n", "############ HASTA AQUÍ LOS DATOS ################################\n", "####################################################################\n", "\n", "load('https://sage.unex.es/501708/simplex2023Auto.sage')\n" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|rr}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} & {b_1} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{5} & \\frac{8}{3} & 0 & 0 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 1 & -\\frac{7}{3} & 4700 & 0 \\\\\n", "{\\color{green}{s}}_{2} & \\frac{2}{3} & 0 & 0 & 0 & -\\frac{2}{3} & 1 & 0 & 1 & 0 & -\\frac{10}{3} & 800 & 0 \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{1}{3} & 0 & 0 & 0 & -\\frac{2}{3} & 0 & 1 & 0 & 0 & -\\frac{4}{3} & 0 & 1 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 & 0 \\\\\n", "{x}_{3} & \\frac{8}{3} & 0 & 1 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 0 & -\\frac{7}{3} & 5100 & 0 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 & 0 \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{350}{3} & 0 & 0 & 0 & -\\frac{700}{3} & 0 & 0 & -200 & 0 & -\\frac{1100}{3} & 4810000 & 0\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|rr}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & 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"[-------+-------------------------------------------------------------------------------+---------------]\n", "[ s5| 8/3 0 0 0 1/3 0 0 2 1 -7/3| 4700 0]\n", "[ s2| 2/3 0 0 0 -2/3 1 0 1 0 -10/3| 800 0]\n", "[ s3| -1/3 0 0 0 -2/3 0 1 0 0 -4/3| 0 1]\n", "[ x2| 0 1 0 0 0 0 0 -1 0 0| 200 0]\n", "[ x3| 8/3 0 1 0 1/3 0 0 2 0 -7/3| 5100 0]\n", "[ x4| 0 0 0 1 0 0 0 0 0 1| 500 0]\n", "[-------+-------------------------------------------------------------------------------+---------------]\n", "[ Z| -350/3 0 0 0 -700/3 0 0 -200 0 -1100/3|4810000 0]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "b1p=matrix(QQ,m,1,[0,0,1,0,0,0]); param1b(b1p) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Apartado c). 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$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\ \\ \\ Fase\\ I}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\ \\ \\ Fase\\ I}$$" ], "text/plain": [ "FI" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{red}{t}}_{4} & {\\color{red}{t}}_{5} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 8 & 6 & 3 & 7 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 20000 \\\\\n", "{\\color{green}{s}}_{2} & 6 & 5 & 2 & 8 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 16000 \\\\\n", "{\\color{green}{s}}_{3} & 5 & 4 & 2 & 6 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 14000 \\\\\n", "{\\color{red}{t}}_{4} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 200 \\\\\n", "{\\color{red}{t}}_{5} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 400 \\\\\n", "{\\color{green}{s}}_{6} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 500 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & -1 & -1 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 600\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{red}{t}}_{4} & {\\color{red}{t}}_{5} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 8 & 6 & 3 & 7 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 20000 \\\\\n", "{\\color{green}{s}}_{2} & 6 & 5 & 2 & 8 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 16000 \\\\\n", "{\\color{green}{s}}_{3} & 5 & 4 & 2 & 6 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 14000 \\\\\n", "{\\color{red}{t}}_{4} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 200 \\\\\n", "{\\color{red}{t}}_{5} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 400 \\\\\n", "{\\color{green}{s}}_{6} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 500 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & -1 & -1 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 600\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 t4 t5| rhs]\n", "[-----+-----------------------------------------------------------------------+-----]\n", "[ s1| 8 6 3 7 1 0 0 0 0 0 0 0|20000]\n", "[ s2| 6 5 2 8 0 1 0 0 0 0 0 0|16000]\n", "[ s3| 5 4 2 6 0 0 1 0 0 0 0 0|14000]\n", "[ t4| 0 1 0 0 0 0 0 -1 0 0 1 0| 200]\n", "[ t5| 0 0 1 0 0 0 0 0 -1 0 0 1| 400]\n", "[ s6| 0 0 0 1 0 0 0 0 0 1 0 0| 500]\n", "[-----+-----------------------------------------------------------------------+-----]\n", "[ W| 0 -1 -1 0 0 0 0 1 1 0 0 0| 600]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 4 , 2 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{red}{t}}_{4} & {\\color{red}{t}}_{5} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 8 & 0 & 3 & 7 & 1 & 0 & 0 & 6 & 0 & 0 & -6 & 0 & 18800 \\\\\n", "{\\color{green}{s}}_{2} & 6 & 0 & 2 & 8 & 0 & 1 & 0 & 5 & 0 & 0 & -5 & 0 & 15000 \\\\\n", "{\\color{green}{s}}_{3} & 5 & 0 & 2 & 6 & 0 & 0 & 1 & 4 & 0 & 0 & -4 & 0 & 13200 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 200 \\\\\n", "{\\color{red}{t}}_{5} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 400 \\\\\n", "{\\color{green}{s}}_{6} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 500 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 400\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{red}{t}}_{4} & {\\color{red}{t}}_{5} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 8 & 0 & 3 & 7 & 1 & 0 & 0 & 6 & 0 & 0 & -6 & 0 & 18800 \\\\\n", "{\\color{green}{s}}_{2} & 6 & 0 & 2 & 8 & 0 & 1 & 0 & 5 & 0 & 0 & -5 & 0 & 15000 \\\\\n", "{\\color{green}{s}}_{3} & 5 & 0 & 2 & 6 & 0 & 0 & 1 & 4 & 0 & 0 & -4 & 0 & 13200 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 200 \\\\\n", "{\\color{red}{t}}_{5} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 400 \\\\\n", "{\\color{green}{s}}_{6} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 500 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 400\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 t4 t5| rhs]\n", "[-----+-----------------------------------------------------------------------+-----]\n", "[ s1| 8 0 3 7 1 0 0 6 0 0 -6 0|18800]\n", "[ s2| 6 0 2 8 0 1 0 5 0 0 -5 0|15000]\n", "[ s3| 5 0 2 6 0 0 1 4 0 0 -4 0|13200]\n", "[ x2| 0 1 0 0 0 0 0 -1 0 0 1 0| 200]\n", "[ t5| 0 0 1 0 0 0 0 0 -1 0 0 1| 400]\n", "[ s6| 0 0 0 1 0 0 0 0 0 1 0 0| 500]\n", "[-----+-----------------------------------------------------------------------+-----]\n", "[ W| 0 0 -1 0 0 0 0 0 1 0 1 0| 400]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 5 , 3 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{red}{t}}_{4} & {\\color{red}{t}}_{5} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 8 & 0 & 0 & 7 & 1 & 0 & 0 & 6 & 3 & 0 & -6 & -3 & 17600 \\\\\n", "{\\color{green}{s}}_{2} & 6 & 0 & 0 & 8 & 0 & 1 & 0 & 5 & 2 & 0 & -5 & -2 & 14200 \\\\\n", "{\\color{green}{s}}_{3} & 5 & 0 & 0 & 6 & 0 & 0 & 1 & 4 & 2 & 0 & -4 & -2 & 12400 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 400 \\\\\n", "{\\color{green}{s}}_{6} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 500 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{red}{t}}_{4} & {\\color{red}{t}}_{5} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 8 & 0 & 0 & 7 & 1 & 0 & 0 & 6 & 3 & 0 & -6 & -3 & 17600 \\\\\n", "{\\color{green}{s}}_{2} & 6 & 0 & 0 & 8 & 0 & 1 & 0 & 5 & 2 & 0 & -5 & -2 & 14200 \\\\\n", "{\\color{green}{s}}_{3} & 5 & 0 & 0 & 6 & 0 & 0 & 1 & 4 & 2 & 0 & -4 & -2 & 12400 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 400 \\\\\n", "{\\color{green}{s}}_{6} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 500 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 t4 t5| rhs]\n", "[-----+-----------------------------------------------------------------------+-----]\n", "[ s1| 8 0 0 7 1 0 0 6 3 0 -6 -3|17600]\n", "[ s2| 6 0 0 8 0 1 0 5 2 0 -5 -2|14200]\n", "[ s3| 5 0 0 6 0 0 1 4 2 0 -4 -2|12400]\n", "[ x2| 0 1 0 0 0 0 0 -1 0 0 1 0| 200]\n", "[ x3| 0 0 1 0 0 0 0 0 -1 0 0 1| 400]\n", "[ s6| 0 0 0 1 0 0 0 0 0 1 0 0| 500]\n", "[-----+-----------------------------------------------------------------------+-----]\n", "[ W| 0 0 0 0 0 0 0 0 0 0 1 1| 0]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "El problema de la fase I es óptimo y Wopt=0. Por tanto, el original es factible\n", "Preparemos el cuadro inicial de la fase II\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\ \\ \\ Fase\\ II}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\ \\ \\ Fase\\ II}$$" ], "text/plain": [ "FII" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " 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{x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 8 & 0 & 0 & 7 & 1 & 0 & 0 & 6 & 3 & 0 & 17600 \\\\\n", "{\\color{green}{s}}_{2} & 6 & 0 & 0 & 8 & 0 & 1 & 0 & 5 & 2 & 0 & 14200 \\\\\n", "{\\color{green}{s}}_{3} & 5 & 0 & 0 & 6 & 0 & 0 & 1 & 4 & 2 & 0 & 12400 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 400 \\\\\n", "{\\color{green}{s}}_{6} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n", "\\hline\n", " {Z_{ind}} & 1750 & 0 & 0 & 2000 & 0 & 0 & 0 & 1200 & 700 & 0 & 520000\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n", "[------+---------------------------------------------------------------------+------]\n", "[ s1| 8 0 0 7 1 0 0 6 3 0| 17600]\n", "[ s2| 6 0 0 8 0 1 0 5 2 0| 14200]\n", "[ s3| 5 0 0 6 0 0 1 4 2 0| 12400]\n", "[ x2| 0 1 0 0 0 0 0 -1 0 0| 200]\n", "[ x3| 0 0 1 0 0 0 0 0 -1 0| 400]\n", "[ s6| 0 0 0 1 0 0 0 0 0 1| 500]\n", "[------+---------------------------------------------------------------------+------]\n", "[ Z| 1750 0 0 2000 0 0 0 1200 700 0|520000]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 6 , 4 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 8 & 0 & 0 & 0 & 1 & 0 & 0 & 6 & 3 & -7 & 14100 \\\\\n", "{\\color{green}{s}}_{2} & 6 & 0 & 0 & 0 & 0 & 1 & 0 & 5 & 2 & -8 & 10200 \\\\\n", "{\\color{green}{s}}_{3} & 5 & 0 & 0 & 0 & 0 & 0 & 1 & 4 & 2 & -6 & 9400 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 400 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n", "\\hline\n", " {Z_{ind}} & 1750 & 0 & 0 & 0 & 0 & 0 & 0 & 1200 & 700 & -2000 & 1520000\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 8 & 0 & 0 & 0 & 1 & 0 & 0 & 6 & 3 & -7 & 14100 \\\\\n", "{\\color{green}{s}}_{2} & 6 & 0 & 0 & 0 & 0 & 1 & 0 & 5 & 2 & -8 & 10200 \\\\\n", "{\\color{green}{s}}_{3} & 5 & 0 & 0 & 0 & 0 & 0 & 1 & 4 & 2 & -6 & 9400 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 400 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n", "\\hline\n", " {Z_{ind}} & 1750 & 0 & 0 & 0 & 0 & 0 & 0 & 1200 & 700 & -2000 & 1520000\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n", "[-------+-------------------------------------------------------------------------------+-------]\n", "[ s1| 8 0 0 0 1 0 0 6 3 -7| 14100]\n", "[ s2| 6 0 0 0 0 1 0 5 2 -8| 10200]\n", "[ s3| 5 0 0 0 0 0 1 4 2 -6| 9400]\n", "[ x2| 0 1 0 0 0 0 0 -1 0 0| 200]\n", "[ x3| 0 0 1 0 0 0 0 0 -1 0| 400]\n", "[ x4| 0 0 0 1 0 0 0 0 0 1| 500]\n", "[-------+-------------------------------------------------------------------------------+-------]\n", "[ Z| 1750 0 0 0 0 0 0 1200 700 -2000|1520000]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 2 , 1 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 0 & 0 & 0 & 1 & -\\frac{4}{3} & 0 & -\\frac{2}{3} & \\frac{1}{3} & \\frac{11}{3} & 500 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & \\frac{1}{6} & 0 & \\frac{5}{6} & \\frac{1}{3} & -\\frac{4}{3} & 1700 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & 0 & -\\frac{5}{6} & 1 & -\\frac{1}{6} & \\frac{1}{3} & \\frac{2}{3} & 900 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 400 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & 0 & -\\frac{875}{3} & 0 & -\\frac{775}{3} & \\frac{350}{3} & \\frac{1000}{3} & 4495000\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 0 & 0 & 0 & 1 & -\\frac{4}{3} & 0 & -\\frac{2}{3} & \\frac{1}{3} & \\frac{11}{3} & 500 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & \\frac{1}{6} & 0 & \\frac{5}{6} & \\frac{1}{3} & -\\frac{4}{3} & 1700 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & 0 & -\\frac{5}{6} & 1 & -\\frac{1}{6} & \\frac{1}{3} & \\frac{2}{3} & 900 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 400 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & 0 & -\\frac{875}{3} & 0 & -\\frac{775}{3} & \\frac{350}{3} & \\frac{1000}{3} & 4495000\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n", "[-------+-------------------------------------------------------------------------------+-------]\n", "[ s1| 0 0 0 0 1 -4/3 0 -2/3 1/3 11/3| 500]\n", "[ x1| 1 0 0 0 0 1/6 0 5/6 1/3 -4/3| 1700]\n", "[ s3| 0 0 0 0 0 -5/6 1 -1/6 1/3 2/3| 900]\n", "[ x2| 0 1 0 0 0 0 0 -1 0 0| 200]\n", "[ x3| 0 0 1 0 0 0 0 0 -1 0| 400]\n", "[ x4| 0 0 0 1 0 0 0 0 0 1| 500]\n", "[-------+-------------------------------------------------------------------------------+-------]\n", "[ Z| 0 0 0 0 0 -875/3 0 -775/3 350/3 1000/3|4495000]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 1 , 10 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{6} & 0 & 0 & 0 & 0 & \\frac{3}{11} & -\\frac{4}{11} & 0 & -\\frac{2}{11} & \\frac{1}{11} & 1 & \\frac{1500}{11} \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & \\frac{4}{11} & -\\frac{7}{22} & 0 & \\frac{13}{22} & \\frac{5}{11} & 0 & \\frac{20700}{11} \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & -\\frac{2}{11} & -\\frac{13}{22} & 1 & -\\frac{1}{22} & \\frac{3}{11} & 0 & \\frac{8900}{11} \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 400 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & -\\frac{3}{11} & \\frac{4}{11} & 0 & \\frac{2}{11} & -\\frac{1}{11} & 0 & \\frac{4000}{11} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & -\\frac{1000}{11} & -\\frac{1875}{11} & 0 & -\\frac{2175}{11} & \\frac{950}{11} & 0 & \\frac{49945000}{11}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{6} & 0 & 0 & 0 & 0 & \\frac{3}{11} & -\\frac{4}{11} & 0 & -\\frac{2}{11} & \\frac{1}{11} & 1 & \\frac{1500}{11} \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & \\frac{4}{11} & -\\frac{7}{22} & 0 & \\frac{13}{22} & \\frac{5}{11} & 0 & \\frac{20700}{11} \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & -\\frac{2}{11} & -\\frac{13}{22} & 1 & -\\frac{1}{22} & \\frac{3}{11} & 0 & \\frac{8900}{11} \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 400 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & -\\frac{3}{11} & \\frac{4}{11} & 0 & \\frac{2}{11} & -\\frac{1}{11} & 0 & \\frac{4000}{11} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & -\\frac{1000}{11} & -\\frac{1875}{11} & 0 & -\\frac{2175}{11} & \\frac{950}{11} & 0 & \\frac{49945000}{11}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n", "[-----------+-----------------------------------------------------------------------------------------------------------------------+-----------]\n", "[ s6| 0 0 0 0 3/11 -4/11 0 -2/11 1/11 1| 1500/11]\n", "[ x1| 1 0 0 0 4/11 -7/22 0 13/22 5/11 0| 20700/11]\n", "[ s3| 0 0 0 0 -2/11 -13/22 1 -1/22 3/11 0| 8900/11]\n", "[ x2| 0 1 0 0 0 0 0 -1 0 0| 200]\n", "[ x3| 0 0 1 0 0 0 0 0 -1 0| 400]\n", "[ x4| 0 0 0 1 -3/11 4/11 0 2/11 -1/11 0| 4000/11]\n", "[-----------+-----------------------------------------------------------------------------------------------------------------------+-----------]\n", "[ Z| 0 0 0 0 -1000/11 -1875/11 0 -2175/11 950/11 0|49945000/11]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 1 , 9 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{5} & 0 & 0 & 0 & 0 & 3 & -4 & 0 & -2 & 1 & 11 & 1500 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & -1 & \\frac{3}{2} & 0 & \\frac{3}{2} & 0 & -5 & 1200 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & -1 & \\frac{1}{2} & 1 & \\frac{1}{2} & 0 & -3 & 400 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 3 & -4 & 0 & -2 & 0 & 11 & 1900 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & -350 & 175 & 0 & -25 & 0 & -950 & 4670000\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{5} & 0 & 0 & 0 & 0 & 3 & -4 & 0 & -2 & 1 & 11 & 1500 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & -1 & \\frac{3}{2} & 0 & \\frac{3}{2} & 0 & -5 & 1200 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & -1 & \\frac{1}{2} & 1 & \\frac{1}{2} & 0 & -3 & 400 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 3 & -4 & 0 & -2 & 0 & 11 & 1900 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & -350 & 175 & 0 & -25 & 0 & -950 & 4670000\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n", "[-------+-------------------------------------------------------------------------------+-------]\n", "[ s5| 0 0 0 0 3 -4 0 -2 1 11| 1500]\n", "[ x1| 1 0 0 0 -1 3/2 0 3/2 0 -5| 1200]\n", "[ s3| 0 0 0 0 -1 1/2 1 1/2 0 -3| 400]\n", "[ x2| 0 1 0 0 0 0 0 -1 0 0| 200]\n", "[ x3| 0 0 1 0 3 -4 0 -2 0 11| 1900]\n", "[ x4| 0 0 0 1 0 0 0 0 0 1| 500]\n", "[-------+-------------------------------------------------------------------------------+-------]\n", "[ Z| 0 0 0 0 -350 175 0 -25 0 -950|4670000]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 2 , 6 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{5} & \\frac{8}{3} & 0 & 0 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 1 & -\\frac{7}{3} & 4700 \\\\\n", "{\\color{green}{s}}_{2} & \\frac{2}{3} & 0 & 0 & 0 & -\\frac{2}{3} & 1 & 0 & 1 & 0 & -\\frac{10}{3} & 800 \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{1}{3} & 0 & 0 & 0 & -\\frac{2}{3} & 0 & 1 & 0 & 0 & -\\frac{4}{3} & 0 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & \\frac{8}{3} & 0 & 1 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 0 & -\\frac{7}{3} & 5100 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{350}{3} & 0 & 0 & 0 & -\\frac{700}{3} & 0 & 0 & -200 & 0 & -\\frac{1100}{3} & 4810000\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{5} & \\frac{8}{3} & 0 & 0 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 1 & -\\frac{7}{3} & 4700 \\\\\n", "{\\color{green}{s}}_{2} & \\frac{2}{3} & 0 & 0 & 0 & -\\frac{2}{3} & 1 & 0 & 1 & 0 & -\\frac{10}{3} & 800 \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{1}{3} & 0 & 0 & 0 & -\\frac{2}{3} & 0 & 1 & 0 & 0 & -\\frac{4}{3} & 0 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & \\frac{8}{3} & 0 & 1 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 0 & -\\frac{7}{3} & 5100 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{350}{3} & 0 & 0 & 0 & -\\frac{700}{3} & 0 & 0 & -200 & 0 & -\\frac{1100}{3} & 4810000\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n", "[-------+-------------------------------------------------------------------------------+-------]\n", "[ s5| 8/3 0 0 0 1/3 0 0 2 1 -7/3| 4700]\n", "[ s2| 2/3 0 0 0 -2/3 1 0 1 0 -10/3| 800]\n", "[ s3| -1/3 0 0 0 -2/3 0 1 0 0 -4/3| 0]\n", "[ x2| 0 1 0 0 0 0 0 -1 0 0| 200]\n", "[ x3| 8/3 0 1 0 1/3 0 0 2 0 -7/3| 5100]\n", "[ x4| 0 0 0 1 0 0 0 0 0 1| 500]\n", "[-------+-------------------------------------------------------------------------------+-------]\n", "[ Z| -350/3 0 0 0 -700/3 0 0 -200 0 -1100/3|4810000]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "El problema es óptimo\n" ] } ], "source": [ "tipo='max' # max o min\n", "\n", "n=4 # número de variables x's\n", "m=6 # número de restricciones (distintas de las de signo)\n", "\n", "c=matrix(QQ,1,n,[1750,1200,700,2000] ) # vector de costos\n", "\n", "A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n", "[8,6,3,7],\n", "[6,5,2,8],\n", "[5,4,2,6],\n", "[0,1,0,0],\n", "[0,0,1,0],\n", "[0,0,0,1]\n", "])\n", "\n", "b=matrix(QQ,m,1,[20000,16000,14000,200,400,500]) # vector de la derecha\n", "\n", "\n", "######################################################\n", "############### VARIABLES DE HOLGURA ################\n", "\n", "\n", "h=matrix(ZZ,1,m,[1,1,1,-1,-1,1]) # variables de holgura: \n", " # Pon 1 si va sumando, \n", " # -1 si va restando y \n", " # 0 si no hay variable de holgura.\n", "\n", "\n", "\n", "\n", "####################################################################\n", "############ HASTA AQUÍ LOS DATOS ################################\n", "####################################################################\n", "\n", "load('https://sage.unex.es/501708/simplex2023Auto.sage')\n", "#load('https://sage.unex.es/501708/simplex2023AutoREVISED.sage')\n", "#load('https://sage.unex.es/501708/simplex2023CompletamenteManual.sage'" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|rr}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} & {b_1} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{5} & \\frac{8}{3} & 0 & 0 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 1 & -\\frac{7}{3} & 4700 & -2 \\\\\n", "{\\color{green}{s}}_{2} & \\frac{2}{3} & 0 & 0 & 0 & -\\frac{2}{3} & 1 & 0 & 1 & 0 & -\\frac{10}{3} & 800 & -1 \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{1}{3} & 0 & 0 & 0 & -\\frac{2}{3} & 0 & 1 & 0 & 0 & -\\frac{4}{3} & 0 & 0 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 & 1 \\\\\n", "{x}_{3} & \\frac{8}{3} & 0 & 1 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 0 & -\\frac{7}{3} & 5100 & -2 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 & 0 \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{350}{3} & 0 & 0 & 0 & -\\frac{700}{3} & 0 & 0 & -200 & 0 & -\\frac{1100}{3} & 4810000 & -200\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|rr}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} & {b_1} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{5} & \\frac{8}{3} & 0 & 0 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 1 & -\\frac{7}{3} & 4700 & -2 \\\\\n", "{\\color{green}{s}}_{2} & \\frac{2}{3} & 0 & 0 & 0 & -\\frac{2}{3} & 1 & 0 & 1 & 0 & -\\frac{10}{3} & 800 & -1 \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{1}{3} & 0 & 0 & 0 & -\\frac{2}{3} & 0 & 1 & 0 & 0 & -\\frac{4}{3} & 0 & 0 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 & 1 \\\\\n", "{x}_{3} & \\frac{8}{3} & 0 & 1 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 0 & -\\frac{7}{3} & 5100 & -2 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 & 0 \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{350}{3} & 0 & 0 & 0 & -\\frac{700}{3} & 0 & 0 & -200 & 0 & -\\frac{1100}{3} & 4810000 & -200\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs rhs1]\n", "[-------+-------------------------------------------------------------------------------+---------------]\n", "[ s5| 8/3 0 0 0 1/3 0 0 2 1 -7/3| 4700 -2]\n", "[ s2| 2/3 0 0 0 -2/3 1 0 1 0 -10/3| 800 -1]\n", "[ s3| -1/3 0 0 0 -2/3 0 1 0 0 -4/3| 0 0]\n", "[ x2| 0 1 0 0 0 0 0 -1 0 0| 200 1]\n", "[ x3| 8/3 0 1 0 1/3 0 0 2 0 -7/3| 5100 -2]\n", "[ x4| 0 0 0 1 0 0 0 0 0 1| 500 0]\n", "[-------+-------------------------------------------------------------------------------+---------------]\n", "[ Z| -350/3 0 0 0 -700/3 0 0 -200 0 -1100/3|4810000 -200]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "bp=matrix(QQ,m,1,[0,0,0,1,0,0]); param1b(bp)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Apartado e) Añadir $x_1 \\geq 0$" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { 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-1 -1 0 0 0 0 1 1 0 0 0| 600]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 4 , 2 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{red}{t}}_{4} & {\\color{red}{t}}_{5} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 8 & 0 & 3 & 7 & 1 & 0 & 0 & 6 & 0 & 0 & -6 & 0 & 18800 \\\\\n", "{\\color{green}{s}}_{2} & 6 & 0 & 2 & 8 & 0 & 1 & 0 & 5 & 0 & 0 & -5 & 0 & 15000 \\\\\n", "{\\color{green}{s}}_{3} & 5 & 0 & 2 & 6 & 0 & 0 & 1 & 4 & 0 & 0 & -4 & 0 & 13200 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 200 \\\\\n", "{\\color{red}{t}}_{5} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 400 \\\\\n", 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& 400 \\\\\n", "{\\color{green}{s}}_{6} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 500 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 400\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 t4 t5| rhs]\n", "[-----+-----------------------------------------------------------------------+-----]\n", "[ s1| 8 0 3 7 1 0 0 6 0 0 -6 0|18800]\n", "[ s2| 6 0 2 8 0 1 0 5 0 0 -5 0|15000]\n", "[ s3| 5 0 2 6 0 0 1 4 0 0 -4 0|13200]\n", "[ x2| 0 1 0 0 0 0 0 -1 0 0 1 0| 200]\n", "[ t5| 0 0 1 0 0 0 0 0 -1 0 0 1| 400]\n", "[ s6| 0 0 0 1 0 0 0 0 0 1 0 0| 500]\n", "[-----+-----------------------------------------------------------------------+-----]\n", "[ W| 0 0 -1 0 0 0 0 0 1 0 1 0| 400]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 5 , 3 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{red}{t}}_{4} & {\\color{red}{t}}_{5} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 8 & 0 & 0 & 7 & 1 & 0 & 0 & 6 & 3 & 0 & -6 & -3 & 17600 \\\\\n", "{\\color{green}{s}}_{2} & 6 & 0 & 0 & 8 & 0 & 1 & 0 & 5 & 2 & 0 & -5 & -2 & 14200 \\\\\n", "{\\color{green}{s}}_{3} & 5 & 0 & 0 & 6 & 0 & 0 & 1 & 4 & 2 & 0 & -4 & -2 & 12400 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 400 \\\\\n", "{\\color{green}{s}}_{6} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 500 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{red}{t}}_{4} & {\\color{red}{t}}_{5} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 8 & 0 & 0 & 7 & 1 & 0 & 0 & 6 & 3 & 0 & -6 & -3 & 17600 \\\\\n", "{\\color{green}{s}}_{2} & 6 & 0 & 0 & 8 & 0 & 1 & 0 & 5 & 2 & 0 & -5 & -2 & 14200 \\\\\n", "{\\color{green}{s}}_{3} & 5 & 0 & 0 & 6 & 0 & 0 & 1 & 4 & 2 & 0 & -4 & -2 & 12400 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 400 \\\\\n", "{\\color{green}{s}}_{6} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 500 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 t4 t5| rhs]\n", "[-----+-----------------------------------------------------------------------+-----]\n", "[ s1| 8 0 0 7 1 0 0 6 3 0 -6 -3|17600]\n", "[ s2| 6 0 0 8 0 1 0 5 2 0 -5 -2|14200]\n", "[ s3| 5 0 0 6 0 0 1 4 2 0 -4 -2|12400]\n", "[ x2| 0 1 0 0 0 0 0 -1 0 0 1 0| 200]\n", "[ x3| 0 0 1 0 0 0 0 0 -1 0 0 1| 400]\n", "[ s6| 0 0 0 1 0 0 0 0 0 1 0 0| 500]\n", "[-----+-----------------------------------------------------------------------+-----]\n", "[ W| 0 0 0 0 0 0 0 0 0 0 1 1| 0]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "El problema de la fase I es óptimo y Wopt=0. Por tanto, el original es factible\n", "Preparemos el cuadro inicial de la fase II\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\ \\ \\ Fase\\ II}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\ \\ \\ Fase\\ II}$$" ], "text/plain": [ "FII" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " 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{x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 8 & 0 & 0 & 7 & 1 & 0 & 0 & 6 & 3 & 0 & 17600 \\\\\n", "{\\color{green}{s}}_{2} & 6 & 0 & 0 & 8 & 0 & 1 & 0 & 5 & 2 & 0 & 14200 \\\\\n", "{\\color{green}{s}}_{3} & 5 & 0 & 0 & 6 & 0 & 0 & 1 & 4 & 2 & 0 & 12400 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 400 \\\\\n", "{\\color{green}{s}}_{6} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n", "\\hline\n", " {Z_{ind}} & 1750 & 0 & 0 & 2000 & 0 & 0 & 0 & 1200 & 700 & 0 & 520000\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n", "[------+---------------------------------------------------------------------+------]\n", "[ s1| 8 0 0 7 1 0 0 6 3 0| 17600]\n", "[ s2| 6 0 0 8 0 1 0 5 2 0| 14200]\n", "[ s3| 5 0 0 6 0 0 1 4 2 0| 12400]\n", "[ x2| 0 1 0 0 0 0 0 -1 0 0| 200]\n", "[ x3| 0 0 1 0 0 0 0 0 -1 0| 400]\n", "[ s6| 0 0 0 1 0 0 0 0 0 1| 500]\n", "[------+---------------------------------------------------------------------+------]\n", "[ Z| 1750 0 0 2000 0 0 0 1200 700 0|520000]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 6 , 4 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 8 & 0 & 0 & 0 & 1 & 0 & 0 & 6 & 3 & -7 & 14100 \\\\\n", "{\\color{green}{s}}_{2} & 6 & 0 & 0 & 0 & 0 & 1 & 0 & 5 & 2 & -8 & 10200 \\\\\n", "{\\color{green}{s}}_{3} & 5 & 0 & 0 & 0 & 0 & 0 & 1 & 4 & 2 & -6 & 9400 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 400 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n", "\\hline\n", " {Z_{ind}} & 1750 & 0 & 0 & 0 & 0 & 0 & 0 & 1200 & 700 & -2000 & 1520000\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 8 & 0 & 0 & 0 & 1 & 0 & 0 & 6 & 3 & -7 & 14100 \\\\\n", "{\\color{green}{s}}_{2} & 6 & 0 & 0 & 0 & 0 & 1 & 0 & 5 & 2 & -8 & 10200 \\\\\n", "{\\color{green}{s}}_{3} & 5 & 0 & 0 & 0 & 0 & 0 & 1 & 4 & 2 & -6 & 9400 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 400 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n", "\\hline\n", " {Z_{ind}} & 1750 & 0 & 0 & 0 & 0 & 0 & 0 & 1200 & 700 & -2000 & 1520000\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n", "[-------+-------------------------------------------------------------------------------+-------]\n", "[ s1| 8 0 0 0 1 0 0 6 3 -7| 14100]\n", "[ s2| 6 0 0 0 0 1 0 5 2 -8| 10200]\n", "[ s3| 5 0 0 0 0 0 1 4 2 -6| 9400]\n", "[ x2| 0 1 0 0 0 0 0 -1 0 0| 200]\n", "[ x3| 0 0 1 0 0 0 0 0 -1 0| 400]\n", "[ x4| 0 0 0 1 0 0 0 0 0 1| 500]\n", "[-------+-------------------------------------------------------------------------------+-------]\n", "[ Z| 1750 0 0 0 0 0 0 1200 700 -2000|1520000]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 2 , 1 )\n" ] }, { "data": { "text/html": [ " 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4495000\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 0 & 0 & 0 & 1 & -\\frac{4}{3} & 0 & -\\frac{2}{3} & \\frac{1}{3} & \\frac{11}{3} & 500 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & \\frac{1}{6} & 0 & \\frac{5}{6} & \\frac{1}{3} & -\\frac{4}{3} & 1700 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & 0 & -\\frac{5}{6} & 1 & -\\frac{1}{6} & \\frac{1}{3} & \\frac{2}{3} & 900 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 400 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & 0 & -\\frac{875}{3} & 0 & -\\frac{775}{3} & \\frac{350}{3} & \\frac{1000}{3} & 4495000\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n", "[-------+-------------------------------------------------------------------------------+-------]\n", "[ s1| 0 0 0 0 1 -4/3 0 -2/3 1/3 11/3| 500]\n", "[ x1| 1 0 0 0 0 1/6 0 5/6 1/3 -4/3| 1700]\n", "[ s3| 0 0 0 0 0 -5/6 1 -1/6 1/3 2/3| 900]\n", "[ x2| 0 1 0 0 0 0 0 -1 0 0| 200]\n", "[ x3| 0 0 1 0 0 0 0 0 -1 0| 400]\n", "[ x4| 0 0 0 1 0 0 0 0 0 1| 500]\n", "[-------+-------------------------------------------------------------------------------+-------]\n", "[ Z| 0 0 0 0 0 -875/3 0 -775/3 350/3 1000/3|4495000]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 1 , 10 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{6} & 0 & 0 & 0 & 0 & \\frac{3}{11} & -\\frac{4}{11} & 0 & -\\frac{2}{11} & \\frac{1}{11} & 1 & \\frac{1500}{11} \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & \\frac{4}{11} & -\\frac{7}{22} & 0 & \\frac{13}{22} & \\frac{5}{11} & 0 & \\frac{20700}{11} \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & -\\frac{2}{11} & -\\frac{13}{22} & 1 & -\\frac{1}{22} & \\frac{3}{11} & 0 & \\frac{8900}{11} \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 400 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & -\\frac{3}{11} & \\frac{4}{11} & 0 & \\frac{2}{11} & -\\frac{1}{11} & 0 & \\frac{4000}{11} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & -\\frac{1000}{11} & -\\frac{1875}{11} & 0 & -\\frac{2175}{11} & \\frac{950}{11} & 0 & \\frac{49945000}{11}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{6} & 0 & 0 & 0 & 0 & \\frac{3}{11} & -\\frac{4}{11} & 0 & -\\frac{2}{11} & \\frac{1}{11} & 1 & \\frac{1500}{11} \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & \\frac{4}{11} & -\\frac{7}{22} & 0 & \\frac{13}{22} & \\frac{5}{11} & 0 & \\frac{20700}{11} \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & -\\frac{2}{11} & -\\frac{13}{22} & 1 & -\\frac{1}{22} & \\frac{3}{11} & 0 & \\frac{8900}{11} \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 400 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & -\\frac{3}{11} & \\frac{4}{11} & 0 & \\frac{2}{11} & -\\frac{1}{11} & 0 & \\frac{4000}{11} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & -\\frac{1000}{11} & -\\frac{1875}{11} & 0 & -\\frac{2175}{11} & \\frac{950}{11} & 0 & \\frac{49945000}{11}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n", "[-----------+-----------------------------------------------------------------------------------------------------------------------+-----------]\n", "[ s6| 0 0 0 0 3/11 -4/11 0 -2/11 1/11 1| 1500/11]\n", "[ x1| 1 0 0 0 4/11 -7/22 0 13/22 5/11 0| 20700/11]\n", "[ s3| 0 0 0 0 -2/11 -13/22 1 -1/22 3/11 0| 8900/11]\n", "[ x2| 0 1 0 0 0 0 0 -1 0 0| 200]\n", "[ x3| 0 0 1 0 0 0 0 0 -1 0| 400]\n", "[ x4| 0 0 0 1 -3/11 4/11 0 2/11 -1/11 0| 4000/11]\n", "[-----------+-----------------------------------------------------------------------------------------------------------------------+-----------]\n", "[ Z| 0 0 0 0 -1000/11 -1875/11 0 -2175/11 950/11 0|49945000/11]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 1 , 9 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{5} & 0 & 0 & 0 & 0 & 3 & -4 & 0 & -2 & 1 & 11 & 1500 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & -1 & \\frac{3}{2} & 0 & \\frac{3}{2} & 0 & -5 & 1200 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & -1 & \\frac{1}{2} & 1 & \\frac{1}{2} & 0 & -3 & 400 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 3 & -4 & 0 & -2 & 0 & 11 & 1900 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & -350 & 175 & 0 & -25 & 0 & -950 & 4670000\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{5} & 0 & 0 & 0 & 0 & 3 & -4 & 0 & -2 & 1 & 11 & 1500 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & -1 & \\frac{3}{2} & 0 & \\frac{3}{2} & 0 & -5 & 1200 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & -1 & \\frac{1}{2} & 1 & \\frac{1}{2} & 0 & -3 & 400 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 3 & -4 & 0 & -2 & 0 & 11 & 1900 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & -350 & 175 & 0 & -25 & 0 & -950 & 4670000\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n", "[-------+-------------------------------------------------------------------------------+-------]\n", "[ s5| 0 0 0 0 3 -4 0 -2 1 11| 1500]\n", "[ x1| 1 0 0 0 -1 3/2 0 3/2 0 -5| 1200]\n", "[ s3| 0 0 0 0 -1 1/2 1 1/2 0 -3| 400]\n", "[ x2| 0 1 0 0 0 0 0 -1 0 0| 200]\n", "[ x3| 0 0 1 0 3 -4 0 -2 0 11| 1900]\n", "[ x4| 0 0 0 1 0 0 0 0 0 1| 500]\n", "[-------+-------------------------------------------------------------------------------+-------]\n", "[ Z| 0 0 0 0 -350 175 0 -25 0 -950|4670000]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 2 , 6 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{5} & \\frac{8}{3} & 0 & 0 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 1 & -\\frac{7}{3} & 4700 \\\\\n", "{\\color{green}{s}}_{2} & \\frac{2}{3} & 0 & 0 & 0 & -\\frac{2}{3} & 1 & 0 & 1 & 0 & -\\frac{10}{3} & 800 \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{1}{3} & 0 & 0 & 0 & -\\frac{2}{3} & 0 & 1 & 0 & 0 & -\\frac{4}{3} & 0 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & \\frac{8}{3} & 0 & 1 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 0 & -\\frac{7}{3} & 5100 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{350}{3} & 0 & 0 & 0 & -\\frac{700}{3} & 0 & 0 & -200 & 0 & -\\frac{1100}{3} & 4810000\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{5} & \\frac{8}{3} & 0 & 0 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 1 & -\\frac{7}{3} & 4700 \\\\\n", "{\\color{green}{s}}_{2} & \\frac{2}{3} & 0 & 0 & 0 & -\\frac{2}{3} & 1 & 0 & 1 & 0 & -\\frac{10}{3} & 800 \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{1}{3} & 0 & 0 & 0 & -\\frac{2}{3} & 0 & 1 & 0 & 0 & -\\frac{4}{3} & 0 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & \\frac{8}{3} & 0 & 1 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 0 & -\\frac{7}{3} & 5100 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{350}{3} & 0 & 0 & 0 & -\\frac{700}{3} & 0 & 0 & -200 & 0 & -\\frac{1100}{3} & 4810000\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n", "[-------+-------------------------------------------------------------------------------+-------]\n", "[ s5| 8/3 0 0 0 1/3 0 0 2 1 -7/3| 4700]\n", "[ s2| 2/3 0 0 0 -2/3 1 0 1 0 -10/3| 800]\n", "[ s3| -1/3 0 0 0 -2/3 0 1 0 0 -4/3| 0]\n", "[ x2| 0 1 0 0 0 0 0 -1 0 0| 200]\n", "[ x3| 8/3 0 1 0 1/3 0 0 2 0 -7/3| 5100]\n", "[ x4| 0 0 0 1 0 0 0 0 0 1| 500]\n", "[-------+-------------------------------------------------------------------------------+-------]\n", "[ Z| -350/3 0 0 0 -700/3 0 0 -200 0 -1100/3|4810000]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "El problema es óptimo\n" ] } ], "source": [ "tipo='max' # max o min\n", "\n", "n=4 # número de variables x's\n", "m=6 # número de restricciones (distintas de las de signo)\n", "\n", "c=matrix(QQ,1,n,[1750,1200,700,2000] ) # vector de costos\n", "\n", "A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n", "[8,6,3,7],\n", "[6,5,2,8],\n", "[5,4,2,6],\n", "[0,1,0,0],\n", "[0,0,1,0],\n", "[0,0,0,1]\n", "])\n", "\n", "b=matrix(QQ,m,1,[20000,16000,14000,200,400,500]) # vector de la derecha\n", "\n", "\n", "######################################################\n", "############### VARIABLES DE HOLGURA ################\n", "\n", "\n", "h=matrix(ZZ,1,m,[1,1,1,-1,-1,1]) # variables de holgura: \n", " # Pon 1 si va sumando, \n", " # -1 si va restando y \n", " # 0 si no hay variable de holgura.\n", "\n", "\n", "\n", "\n", "####################################################################\n", "############ HASTA AQUÍ LOS DATOS ################################\n", "####################################################################\n", "\n", "load('https://sage.unex.es/501708/simplex2023Auto.sage')\n", "#load('https://sage.unex.es/501708/simplex2023AutoREVISED.sage')\n", "#load('https://sage.unex.es/501708/simplex2023CompletamenteManual.sage'" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "10" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nv" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{5} & \\frac{8}{3} & 0 & 0 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 1 & -\\frac{7}{3} & 0 & 4700 \\\\\n", "{\\color{green}{s}}_{2} & \\frac{2}{3} & 0 & 0 & 0 & -\\frac{2}{3} & 1 & 0 & 1 & 0 & -\\frac{10}{3} & 0 & 800 \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{1}{3} & 0 & 0 & 0 & -\\frac{2}{3} & 0 & 1 & 0 & 0 & -\\frac{4}{3} & 0 & 0 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 200 \\\\\n", "{x}_{3} & \\frac{8}{3} & 0 & 1 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 0 & -\\frac{7}{3} & 0 & 5100 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 500 \\\\\n", "{\\color{green}{s}}_{7} & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -100 \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{350}{3} & 0 & 0 & 0 & -\\frac{700}{3} & 0 & 0 & -200 & 0 & -\\frac{1100}{3} & 0 & 4810000\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{5} & \\frac{8}{3} & 0 & 0 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 1 & -\\frac{7}{3} & 0 & 4700 \\\\\n", "{\\color{green}{s}}_{2} & \\frac{2}{3} & 0 & 0 & 0 & -\\frac{2}{3} & 1 & 0 & 1 & 0 & -\\frac{10}{3} & 0 & 800 \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{1}{3} & 0 & 0 & 0 & -\\frac{2}{3} & 0 & 1 & 0 & 0 & -\\frac{4}{3} & 0 & 0 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 200 \\\\\n", "{x}_{3} & \\frac{8}{3} & 0 & 1 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 0 & -\\frac{7}{3} & 0 & 5100 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 500 \\\\\n", "{\\color{green}{s}}_{7} & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -100 \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{350}{3} & 0 & 0 & 0 & -\\frac{700}{3} & 0 & 0 & -200 & 0 & -\\frac{1100}{3} & 0 & 4810000\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7| rhs]\n", "[-------+---------------------------------------------------------------------------------------+-------]\n", "[ s5| 8/3 0 0 0 1/3 0 0 2 1 -7/3 0| 4700]\n", "[ s2| 2/3 0 0 0 -2/3 1 0 1 0 -10/3 0| 800]\n", "[ s3| -1/3 0 0 0 -2/3 0 1 0 0 -4/3 0| 0]\n", "[ x2| 0 1 0 0 0 0 0 -1 0 0 0| 200]\n", "[ x3| 8/3 0 1 0 1/3 0 0 2 0 -7/3 0| 5100]\n", "[ x4| 0 0 0 1 0 0 0 0 0 1 0| 500]\n", "[ s7| -1 0 0 0 0 0 0 0 0 0 1| -100]\n", "[-------+---------------------------------------------------------------------------------------+-------]\n", "[ Z| -350/3 0 0 0 -700/3 0 0 -200 0 -1100/3 0|4810000]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "v=matrix(QQ,1,nv,[-1,0,0,0,0,0,0,0,0,0] ); R=-100;\n", "añadeRes(v,R)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{5} & 0 & 0 & 0 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 1 & -\\frac{7}{3} & \\frac{8}{3} & \\frac{13300}{3} \\\\\n", "{\\color{green}{s}}_{2} & 0 & 0 & 0 & 0 & -\\frac{2}{3} & 1 & 0 & 1 & 0 & -\\frac{10}{3} & \\frac{2}{3} & \\frac{2200}{3} \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & -\\frac{2}{3} & 0 & 1 & 0 & 0 & -\\frac{4}{3} & -\\frac{1}{3} & \\frac{100}{3} \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 0 & -\\frac{7}{3} & \\frac{8}{3} & \\frac{14500}{3} \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 500 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 100 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & -\\frac{700}{3} & 0 & 0 & -200 & 0 & -\\frac{1100}{3} & -\\frac{350}{3} & \\frac{14395000}{3}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{5} & 0 & 0 & 0 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 1 & -\\frac{7}{3} & \\frac{8}{3} & \\frac{13300}{3} \\\\\n", "{\\color{green}{s}}_{2} & 0 & 0 & 0 & 0 & -\\frac{2}{3} & 1 & 0 & 1 & 0 & -\\frac{10}{3} & \\frac{2}{3} & \\frac{2200}{3} \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & -\\frac{2}{3} & 0 & 1 & 0 & 0 & -\\frac{4}{3} & -\\frac{1}{3} & \\frac{100}{3} \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & \\frac{1}{3} & 0 & 0 & 2 & 0 & -\\frac{7}{3} & \\frac{8}{3} & \\frac{14500}{3} \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 500 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 100 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & -\\frac{700}{3} & 0 & 0 & -200 & 0 & -\\frac{1100}{3} & -\\frac{350}{3} & \\frac{14395000}{3}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7| rhs]\n", "[----------+------------------------------------------------------------------------------------------------------------------------+----------]\n", "[ s5| 0 0 0 0 1/3 0 0 2 1 -7/3 8/3| 13300/3]\n", "[ s2| 0 0 0 0 -2/3 1 0 1 0 -10/3 2/3| 2200/3]\n", "[ s3| 0 0 0 0 -2/3 0 1 0 0 -4/3 -1/3| 100/3]\n", "[ x2| 0 1 0 0 0 0 0 -1 0 0 0| 200]\n", "[ x3| 0 0 1 0 1/3 0 0 2 0 -7/3 8/3| 14500/3]\n", "[ x4| 0 0 0 1 0 0 0 0 0 1 0| 500]\n", "[ x1| 1 0 0 0 0 0 0 0 0 0 -1| 100]\n", "[----------+------------------------------------------------------------------------------------------------------------------------+----------]\n", "[ Z| 0 0 0 0 -700/3 0 0 -200 0 -1100/3 -350/3|14395000/3]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(7,1)" ] } ], "metadata": { "kernelspec": { "display_name": "SageMath 9.5", "language": "sage", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.2" } }, "nbformat": 4, "nbformat_minor": 4 }