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\\mspace{-6mu}&\\mspace{-6mu} 241 y_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 784 y_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 1166 y_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 1860 y_{4} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 15 y_{5} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 8 y_{6} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 6 y_{7} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 4 y_{8} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 3 y_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 16 y_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 12 y_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 20 y_{4} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{5} \\mspace{-6mu}&\\mspace{-6mu} 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$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {\\color{green}{s}}_{8} & {\\color{red}{t}}_{5} & {\\color{red}{t}}_{6} & {\\color{red}{t}}_{7} & {\\color{red}{t}}_{8} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 3 & 10 & 12 & 8 & -3 & -10 & -12 & -8 & 12 \\\\\n", "{\\color{green}{s}}_{2} & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 16 & 2 & 40 & 50 & -16 & -2 & -40 & -50 & 88 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 12 & 60 & 48 & 35 & -12 & -60 & -48 & -35 & 78 \\\\\n", "{\\color{green}{s}}_{4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 20 & 100 & 80 & 50 & -20 & -100 & -80 & -50 & 80 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 15 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 1 & 0 & 0 & 8 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 1 & 0 & 6 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 1 & 4 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 0\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {\\color{green}{s}}_{8} & {\\color{red}{t}}_{5} & {\\color{red}{t}}_{6} & {\\color{red}{t}}_{7} & {\\color{red}{t}}_{8} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 3 & 10 & 12 & 8 & -3 & -10 & -12 & -8 & 12 \\\\\n", "{\\color{green}{s}}_{2} & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 16 & 2 & 40 & 50 & -16 & -2 & -40 & -50 & 88 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 12 & 60 & 48 & 35 & -12 & -60 & -48 & -35 & 78 \\\\\n", "{\\color{green}{s}}_{4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 20 & 100 & 80 & 50 & -20 & -100 & -80 & -50 & 80 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 15 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 1 & 0 & 0 & 8 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 1 & 0 & 6 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 1 & 4 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 0\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7 s8 t5 t6 t7 t8| rhs]\n", "[----+-------------------------------------------------------------------------------+----]\n", "[ s1| 0 0 0 0 1 0 0 0 3 10 12 8 -3 -10 -12 -8| 12]\n", "[ s2| 0 0 0 0 0 1 0 0 16 2 40 50 -16 -2 -40 -50| 88]\n", "[ s3| 0 0 0 0 0 0 1 0 12 60 48 35 -12 -60 -48 -35| 78]\n", "[ s4| 0 0 0 0 0 0 0 1 20 100 80 50 -20 -100 -80 -50| 80]\n", "[ x1| 1 0 0 0 0 0 0 0 -1 0 0 0 1 0 0 0| 15]\n", "[ x2| 0 1 0 0 0 0 0 0 0 -1 0 0 0 1 0 0| 8]\n", "[ x3| 0 0 1 0 0 0 0 0 0 0 -1 0 0 0 1 0| 6]\n", "[ x4| 0 0 0 1 0 0 0 0 0 0 0 -1 0 0 0 1| 4]\n", "[----+-------------------------------------------------------------------------------+----]\n", "[ W| 0 0 0 0 0 0 0 0 0 0 0 0 1 1 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": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {\\color{green}{s}}_{8} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 3 & 10 & 12 & 8 & 12 \\\\\n", "{\\color{green}{s}}_{2} & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 16 & 2 & 40 & 50 & 88 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 12 & 60 & 48 & 35 & 78 \\\\\n", "{\\color{green}{s}}_{4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 20 & 100 & 80 & 50 & 80 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 15 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 8 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 6 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 4 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 209 & 298 & 264 & 516 & 9167\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {\\color{green}{s}}_{8} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 3 & 10 & 12 & 8 & 12 \\\\\n", "{\\color{green}{s}}_{2} & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 16 & 2 & 40 & 50 & 88 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 12 & 60 & 48 & 35 & 78 \\\\\n", "{\\color{green}{s}}_{4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 20 & 100 & 80 & 50 & 80 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 15 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 8 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 6 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 4 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 209 & 298 & 264 & 516 & 9167\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7 s8| rhs]\n", "[----+-----------------------------------------------------------+----]\n", "[ s1| 0 0 0 0 1 0 0 0 3 10 12 8| 12]\n", "[ s2| 0 0 0 0 0 1 0 0 16 2 40 50| 88]\n", "[ s3| 0 0 0 0 0 0 1 0 12 60 48 35| 78]\n", "[ s4| 0 0 0 0 0 0 0 1 20 100 80 50| 80]\n", "[ x1| 1 0 0 0 0 0 0 0 -1 0 0 0| 15]\n", "[ x2| 0 1 0 0 0 0 0 0 0 -1 0 0| 8]\n", "[ x3| 0 0 1 0 0 0 0 0 0 0 -1 0| 6]\n", "[ x4| 0 0 0 1 0 0 0 0 0 0 0 -1| 4]\n", "[----+-----------------------------------------------------------+----]\n", "[ Z| 0 0 0 0 0 0 0 0 209 298 264 516|9167]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 1 , 12 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {\\color{green}{s}}_{8} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{8} & 0 & 0 & 0 & 0 & \\frac{1}{8} & 0 & 0 & 0 & \\frac{3}{8} & \\frac{5}{4} & \\frac{3}{2} & 1 & \\frac{3}{2} \\\\\n", "{\\color{green}{s}}_{2} & 0 & 0 & 0 & 0 & -\\frac{25}{4} & 1 & 0 & 0 & -\\frac{11}{4} & -\\frac{121}{2} & -35 & 0 & 13 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & -\\frac{35}{8} & 0 & 1 & 0 & -\\frac{9}{8} & \\frac{65}{4} & -\\frac{9}{2} & 0 & \\frac{51}{2} \\\\\n", "{\\color{green}{s}}_{4} & 0 & 0 & 0 & 0 & -\\frac{25}{4} & 0 & 0 & 1 & \\frac{5}{4} & \\frac{75}{2} & 5 & 0 & 5 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 15 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 8 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 6 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & \\frac{1}{8} & 0 & 0 & 0 & \\frac{3}{8} & \\frac{5}{4} & \\frac{3}{2} & 0 & \\frac{11}{2} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & -\\frac{129}{2} & 0 & 0 & 0 & \\frac{31}{2} & -347 & -510 & 0 & 9941\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {\\color{green}{s}}_{8} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{8} & 0 & 0 & 0 & 0 & \\frac{1}{8} & 0 & 0 & 0 & \\frac{3}{8} & \\frac{5}{4} & \\frac{3}{2} & 1 & \\frac{3}{2} \\\\\n", "{\\color{green}{s}}_{2} & 0 & 0 & 0 & 0 & -\\frac{25}{4} & 1 & 0 & 0 & -\\frac{11}{4} & -\\frac{121}{2} & -35 & 0 & 13 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & -\\frac{35}{8} & 0 & 1 & 0 & -\\frac{9}{8} & \\frac{65}{4} & -\\frac{9}{2} & 0 & \\frac{51}{2} \\\\\n", "{\\color{green}{s}}_{4} & 0 & 0 & 0 & 0 & -\\frac{25}{4} & 0 & 0 & 1 & \\frac{5}{4} & \\frac{75}{2} & 5 & 0 & 5 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 15 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 8 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 6 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & \\frac{1}{8} & 0 & 0 & 0 & \\frac{3}{8} & \\frac{5}{4} & \\frac{3}{2} & 0 & \\frac{11}{2} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & -\\frac{129}{2} & 0 & 0 & 0 & \\frac{31}{2} & -347 & -510 & 0 & 9941\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7 s8| rhs]\n", "[------+-----------------------------------------------------------------------------------+------]\n", "[ s8| 0 0 0 0 1/8 0 0 0 3/8 5/4 3/2 1| 3/2]\n", "[ s2| 0 0 0 0 -25/4 1 0 0 -11/4 -121/2 -35 0| 13]\n", "[ s3| 0 0 0 0 -35/8 0 1 0 -9/8 65/4 -9/2 0| 51/2]\n", "[ s4| 0 0 0 0 -25/4 0 0 1 5/4 75/2 5 0| 5]\n", "[ x1| 1 0 0 0 0 0 0 0 -1 0 0 0| 15]\n", "[ x2| 0 1 0 0 0 0 0 0 0 -1 0 0| 8]\n", "[ x3| 0 0 1 0 0 0 0 0 0 0 -1 0| 6]\n", "[ x4| 0 0 0 1 1/8 0 0 0 3/8 5/4 3/2 0| 11/2]\n", "[------+-----------------------------------------------------------------------------------+------]\n", "[ Z| 0 0 0 0 -129/2 0 0 0 31/2 -347 -510 0| 9941]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 1 , 9 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {\\color{green}{s}}_{8} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{5} & 0 & 0 & 0 & 0 & \\frac{1}{3} & 0 & 0 & 0 & 1 & \\frac{10}{3} & 4 & \\frac{8}{3} & 4 \\\\\n", "{\\color{green}{s}}_{2} & 0 & 0 & 0 & 0 & -\\frac{16}{3} & 1 & 0 & 0 & 0 & -\\frac{154}{3} & -24 & \\frac{22}{3} & 24 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & -4 & 0 & 1 & 0 & 0 & 20 & 0 & 3 & 30 \\\\\n", "{\\color{green}{s}}_{4} & 0 & 0 & 0 & 0 & -\\frac{20}{3} & 0 & 0 & 1 & 0 & \\frac{100}{3} & 0 & -\\frac{10}{3} & 0 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & \\frac{1}{3} & 0 & 0 & 0 & 0 & \\frac{10}{3} & 4 & \\frac{8}{3} & 19 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 8 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 6 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 4 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & -\\frac{209}{3} & 0 & 0 & 0 & 0 & -\\frac{1196}{3} & -572 & -\\frac{124}{3} & 10003\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {\\color{green}{s}}_{8} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{5} & 0 & 0 & 0 & 0 & \\frac{1}{3} & 0 & 0 & 0 & 1 & \\frac{10}{3} & 4 & \\frac{8}{3} & 4 \\\\\n", "{\\color{green}{s}}_{2} & 0 & 0 & 0 & 0 & -\\frac{16}{3} & 1 & 0 & 0 & 0 & -\\frac{154}{3} & -24 & \\frac{22}{3} & 24 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & -4 & 0 & 1 & 0 & 0 & 20 & 0 & 3 & 30 \\\\\n", "{\\color{green}{s}}_{4} & 0 & 0 & 0 & 0 & -\\frac{20}{3} & 0 & 0 & 1 & 0 & \\frac{100}{3} & 0 & -\\frac{10}{3} & 0 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & \\frac{1}{3} & 0 & 0 & 0 & 0 & \\frac{10}{3} & 4 & \\frac{8}{3} & 19 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 8 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 6 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 4 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & -\\frac{209}{3} & 0 & 0 & 0 & 0 & -\\frac{1196}{3} & -572 & -\\frac{124}{3} & 10003\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7 s8| rhs]\n", "[-------+-----------------------------------------------------------------------------------------------+-------]\n", "[ s5| 0 0 0 0 1/3 0 0 0 1 10/3 4 8/3| 4]\n", "[ s2| 0 0 0 0 -16/3 1 0 0 0 -154/3 -24 22/3| 24]\n", "[ s3| 0 0 0 0 -4 0 1 0 0 20 0 3| 30]\n", "[ s4| 0 0 0 0 -20/3 0 0 1 0 100/3 0 -10/3| 0]\n", "[ x1| 1 0 0 0 1/3 0 0 0 0 10/3 4 8/3| 19]\n", "[ x2| 0 1 0 0 0 0 0 0 0 -1 0 0| 8]\n", "[ x3| 0 0 1 0 0 0 0 0 0 0 -1 0| 6]\n", "[ x4| 0 0 0 1 0 0 0 0 0 0 0 -1| 4]\n", "[-------+-----------------------------------------------------------------------------------------------+-------]\n", "[ Z| 0 0 0 0 -209/3 0 0 0 0 -1196/3 -572 -124/3| 10003]" ] }, "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=8 # número de restricciones (distintas de las de signo)\n", "\n", "c=matrix(QQ,1,n,[209,298,264,516] ) # vector de costos\n", "\n", "A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n", "[3,10,12,8],\n", "[16,2,40,50],\n", "[12,60,48,35],\n", "[20,100,80,50],\n", "[1,0,0,0],\n", "[0,1,0,0],\n", "[0,0,1,0],\n", "[0,0,0,1]\n", "])\n", "\n", "b=matrix(QQ,m,1,[241,784,1166,1860,15,8,6,4]) # 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,-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/SAGE/simplex2023Auto.sage')\n", "#load('https://sage.unex.es/501708/SAGE/simplex2023AutoREVISED.sage')\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "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 }