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\\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} \\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} 7 y_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 4 y_{3} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{5} \\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} 1200 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 7 y_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 5 y_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 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} y_{6} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 700 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 7 y_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 8 y_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 8 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} + \\mspace{-6mu}&\\mspace{-6mu} y_{7} \\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} \\geq 0,\\ y_{5} \\leq 0,\\ y_{6} \\leq 0,\\ y_{7} \\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}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{22475000}{7}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{22475000}{7}$$" ], "text/plain": [ "22475000/7" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(0,\\,\\frac{1200}{7},\\,0,\\,\\frac{5050}{7},\\,0,\\,-\\frac{1100}{7},\\,\\frac{4400}{7}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(0,\\,\\frac{1200}{7},\\,0,\\,\\frac{5050}{7},\\,0,\\,-\\frac{1100}{7},\\,\\frac{4400}{7}\\right)$$" ], "text/plain": [ "(0, 1200/7, 0, 5050/7, 0, -1100/7, 4400/7)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{}$ " ], "text/latex": [ "$$\\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}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {\\color{red}{t}}_{5} & {\\color{red}{t}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 8 & 6 & 7 & 7 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 20000 \\\\\n", "{\\color{green}{s}}_{2} & 6 & 7 & 5 & 8 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 16000 \\\\\n", "{\\color{green}{s}}_{3} & 4 & 4 & 2 & 8 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 14000 \\\\\n", "{\\color{green}{s}}_{4} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 300 \\\\\n", "{\\color{red}{t}}_{5} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 200 \\\\\n", "{\\color{red}{t}}_{6} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 400 \\\\\n", "{\\color{green}{s}}_{7} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 500 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & -1 & -1 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 600\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrr|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{red}{t}}_{5} & {\\color{red}{t}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 8 & 6 & 7 & 7 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 20000 \\\\\n", "{\\color{green}{s}}_{2} & 6 & 7 & 5 & 8 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 16000 \\\\\n", "{\\color{green}{s}}_{3} & 4 & 4 & 2 & 8 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 14000 \\\\\n", "{\\color{green}{s}}_{4} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 300 \\\\\n", "{\\color{red}{t}}_{5} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 200 \\\\\n", "{\\color{red}{t}}_{6} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 400 \\\\\n", "{\\color{green}{s}}_{7} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 500 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & -1 & -1 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 600\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7 t5 t6| rhs]\n", "[-----+-----------------------------------------------------------------------------+-----]\n", "[ s1| 8 6 7 7 1 0 0 0 0 0 0 0 0|20000]\n", "[ s2| 6 7 5 8 0 1 0 0 0 0 0 0 0|16000]\n", "[ s3| 4 4 2 8 0 0 1 0 0 0 0 0 0|14000]\n", "[ s4| 1 0 0 0 0 0 0 1 0 0 0 0 0| 300]\n", "[ t5| 0 1 0 0 0 0 0 0 -1 0 0 1 0| 200]\n", "[ t6| 0 0 1 0 0 0 0 0 0 -1 0 0 1| 400]\n", "[ s7| 0 0 0 1 0 0 0 0 0 0 1 0 0| 500]\n", "[-----+-----------------------------------------------------------------------------+-----]\n", "[ W| 0 -1 -1 0 0 0 0 0 1 1 0 0 0| 600]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ " \n", " \n", "cambio( 5 , 2 )\n", "cambio( 6 , 3 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {\\color{red}{t}}_{5} & {\\color{red}{t}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 8 & 0 & 0 & 7 & 1 & 0 & 0 & 0 & 6 & 7 & 0 & -6 & -7 & 16000 \\\\\n", "{\\color{green}{s}}_{2} & 6 & 0 & 0 & 8 & 0 & 1 & 0 & 0 & 7 & 5 & 0 & -7 & -5 & 12600 \\\\\n", "{\\color{green}{s}}_{3} & 4 & 0 & 0 & 8 & 0 & 0 & 1 & 0 & 4 & 2 & 0 & -4 & -2 & 12400 \\\\\n", "{\\color{green}{s}}_{4} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 300 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 400 \\\\\n", "{\\color{green}{s}}_{7} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 500 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrr|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{red}{t}}_{5} & {\\color{red}{t}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 8 & 0 & 0 & 7 & 1 & 0 & 0 & 0 & 6 & 7 & 0 & -6 & -7 & 16000 \\\\\n", "{\\color{green}{s}}_{2} & 6 & 0 & 0 & 8 & 0 & 1 & 0 & 0 & 7 & 5 & 0 & -7 & -5 & 12600 \\\\\n", "{\\color{green}{s}}_{3} & 4 & 0 & 0 & 8 & 0 & 0 & 1 & 0 & 4 & 2 & 0 & -4 & -2 & 12400 \\\\\n", "{\\color{green}{s}}_{4} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 300 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 400 \\\\\n", "{\\color{green}{s}}_{7} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 500 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7 t5 t6| rhs]\n", "[-----+-----------------------------------------------------------------------------+-----]\n", "[ s1| 8 0 0 7 1 0 0 0 6 7 0 -6 -7|16000]\n", "[ s2| 6 0 0 8 0 1 0 0 7 5 0 -7 -5|12600]\n", "[ s3| 4 0 0 8 0 0 1 0 4 2 0 -4 -2|12400]\n", "[ s4| 1 0 0 0 0 0 0 1 0 0 0 0 0| 300]\n", "[ x2| 0 1 0 0 0 0 0 0 -1 0 0 1 0| 200]\n", "[ x3| 0 0 1 0 0 0 0 0 0 -1 0 0 1| 400]\n", "[ s7| 0 0 0 1 0 0 0 0 0 0 1 0 0| 500]\n", "[-----+-----------------------------------------------------------------------------+-----]\n", "[ W| 0 0 0 0 0 0 0 0 0 0 0 1 1| 0]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "El problema de la fase I es óptimo y Wopt=0. Por tanto, el original es factible\n", "Preparemos el cuadro inicial de la fase II\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$ " ], "text/latex": [ "$$\\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}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " 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"\\end{array}\\right)$ " ], "text/latex": [ "$$\\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}}_{1} & 8 & 0 & 0 & 7 & 1 & 0 & 0 & 0 & 6 & 7 & 0 & 16000 \\\\\n", "{\\color{green}{s}}_{2} & 6 & 0 & 0 & 8 & 0 & 1 & 0 & 0 & 7 & 5 & 0 & 12600 \\\\\n", "{\\color{green}{s}}_{3} & 4 & 0 & 0 & 8 & 0 & 0 & 1 & 0 & 4 & 2 & 0 & 12400 \\\\\n", "{\\color{green}{s}}_{4} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 300 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 200 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 400 \\\\\n", "{\\color{green}{s}}_{7} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n", "\\hline\n", " {Z_{ind}} & 1750 & 0 & 0 & 2000 & 0 & 0 & 0 & 0 & 1200 & 700 & 0 & 520000\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7| rhs]\n", "[------+----------------------------------------------------------------------------+------]\n", "[ s1| 8 0 0 7 1 0 0 0 6 7 0| 16000]\n", "[ s2| 6 0 0 8 0 1 0 0 7 5 0| 12600]\n", "[ s3| 4 0 0 8 0 0 1 0 4 2 0| 12400]\n", "[ s4| 1 0 0 0 0 0 0 1 0 0 0| 300]\n", "[ x2| 0 1 0 0 0 0 0 0 -1 0 0| 200]\n", "[ x3| 0 0 1 0 0 0 0 0 0 -1 0| 400]\n", "[ s7| 0 0 0 1 0 0 0 0 0 0 1| 500]\n", "[------+----------------------------------------------------------------------------+------]\n", "[ Z| 1750 0 0 2000 0 0 0 0 1200 700 0|520000]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 7 , 4 )\n", "cambio( 4 , 1 )\n", "cambio( 2 , 9 )\n" ] }, { "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}}_{1} & 0 & 0 & 0 & 0 & 1 & -\\frac{6}{7} & 0 & -\\frac{20}{7} & 0 & \\frac{19}{7} & -\\frac{1}{7} & \\frac{29900}{7} \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{7} & 0 & -\\frac{6}{7} & 1 & \\frac{5}{7} & -\\frac{8}{7} & \\frac{6800}{7} \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & 0 & -\\frac{4}{7} & 1 & -\\frac{4}{7} & 0 & -\\frac{6}{7} & -\\frac{24}{7} & \\frac{23200}{7} \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 300 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & \\frac{1}{7} & 0 & -\\frac{6}{7} & 0 & \\frac{5}{7} & -\\frac{8}{7} & \\frac{8200}{7} \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 400 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & 0 & -\\frac{1200}{7} & 0 & -\\frac{5050}{7} & 0 & -\\frac{1100}{7} & -\\frac{4400}{7} & \\frac{22475000}{7}\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}}_{1} & 0 & 0 & 0 & 0 & 1 & -\\frac{6}{7} & 0 & -\\frac{20}{7} & 0 & \\frac{19}{7} & -\\frac{1}{7} & \\frac{29900}{7} \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{7} & 0 & -\\frac{6}{7} & 1 & \\frac{5}{7} & -\\frac{8}{7} & \\frac{6800}{7} \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & 0 & -\\frac{4}{7} & 1 & -\\frac{4}{7} & 0 & -\\frac{6}{7} & -\\frac{24}{7} & \\frac{23200}{7} \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 300 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & \\frac{1}{7} & 0 & -\\frac{6}{7} & 0 & \\frac{5}{7} & -\\frac{8}{7} & \\frac{8200}{7} \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 400 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 500 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & 0 & -\\frac{1200}{7} & 0 & -\\frac{5050}{7} & 0 & -\\frac{1100}{7} & -\\frac{4400}{7} & \\frac{22475000}{7}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7| rhs]\n", "[----------+------------------------------------------------------------------------------------------------------------------------+----------]\n", "[ s1| 0 0 0 0 1 -6/7 0 -20/7 0 19/7 -1/7| 29900/7]\n", "[ s5| 0 0 0 0 0 1/7 0 -6/7 1 5/7 -8/7| 6800/7]\n", "[ s3| 0 0 0 0 0 -4/7 1 -4/7 0 -6/7 -24/7| 23200/7]\n", "[ x1| 1 0 0 0 0 0 0 1 0 0 0| 300]\n", "[ x2| 0 1 0 0 0 1/7 0 -6/7 0 5/7 -8/7| 8200/7]\n", "[ x3| 0 0 1 0 0 0 0 0 0 -1 0| 400]\n", "[ x4| 0 0 0 1 0 0 0 0 0 0 1| 500]\n", "[----------+------------------------------------------------------------------------------------------------------------------------+----------]\n", "[ Z| 0 0 0 0 0 -1200/7 0 -5050/7 0 -1100/7 -4400/7|22475000/7]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "El problema es óptimo\n" ] } ], "source": [ "tipo='max'\n", "\n", "n=4 # número de variables x's\n", "m=7 # 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", "[8,6,7,7],\n", "[6,7,5,8],\n", "[4,4,2,8],\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,[20000,16000,14000,300,200,400,500]) # En miles de unidades. 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]) # 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", "######### Problemas Paramétricos ###########\n", " \n", "prmtr_b=0 # 1 si quieres usar un parámetro en b\n", " # 0 en caso contrario\n", "\n", "bp=matrix(QQ,m,1,[1,0,0,0,0,0,0]) # vector de la derecha para problemas paramétricos.\n", "\n", "###################################################### \n", " \n", "prmtr_c=0 # 1 si quieres usar un parámetro en c\n", " # 0 en caso contrario\n", "\n", " \n", "cp=matrix(QQ,1,n,[0,0,0,0] ) # vector de costos adicional para problemas paramétricos.\n", "\n", "######################################################\n", "\n", "\n", "##############################################################################\n", "####### Usando el paquete de programación lineal Pinteractive de Sage ########\n", "##############################################################################\n", "signos=[]\n", "for i in range(m):\n", " if h[0,i] == -1:\n", " signos.append(\">=\")\n", " elif h[0,i] == 1:\n", " signos.append(\"<=\")\n", " elif h[0,i] == 0:\n", " signos.append(\"==\")\n", "\n", "var_nam = []\n", "for i in range(n):\n", " k=i+1\n", " var_nam.append('x_%s' %k)\n", " \n", " \n", "PPL = InteractiveLPProblem(A, b, c, var_nam,\n", "constraint_type=signos, variable_type=\">=\", problem_type=\"max\") \n", "\n", "##############################################################################\n", "##############################################################################\n", "\n", "\n", "####################################################################\n", "############ HASTA AQUÍ LOS DATOS ################################\n", "####################################################################\n", "\n", "salto=var('salto', latex_name='')\n", "raya=var('ry', latex_name='===================================')\n", "show(ry)\n", "show(ry)\n", "show(PPL)\n", "show(PPL.optimal_value())\n", "show(PPL.optimal_solution())\n", "\n", "#load('https://sage.unex.es/501708/simplex2023Auto.sage')\n", "load('https://sage.unex.es/501708/simplex2023Auto_MC.sage')" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1171.42857142857" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "8200/7." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "########################################\n", "\n", "Añadimos $x_2 \\geq 1172$" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "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 & -\\frac{6}{7} & 0 & -\\frac{20}{7} & 0 & \\frac{19}{7} & -\\frac{1}{7} & 0 & \\frac{29900}{7} \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{7} & 0 & -\\frac{6}{7} & 1 & \\frac{5}{7} & -\\frac{8}{7} & 0 & \\frac{6800}{7} \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & 0 & -\\frac{4}{7} & 1 & -\\frac{4}{7} & 0 & -\\frac{6}{7} & -\\frac{24}{7} & 0 & \\frac{23200}{7} \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 300 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & \\frac{1}{7} & 0 & -\\frac{6}{7} & 0 & \\frac{5}{7} & -\\frac{8}{7} & 0 & \\frac{8200}{7} \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 400 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 500 \\\\\n", "{\\color{green}{s}}_{8} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{7} & 0 & -\\frac{6}{7} & 0 & \\frac{5}{7} & -\\frac{8}{7} & 1 & -\\frac{4}{7} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & 0 & -\\frac{1200}{7} & 0 & -\\frac{5050}{7} & 0 & -\\frac{1100}{7} & -\\frac{4400}{7} & 0 & \\frac{22475000}{7}\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 & -\\frac{6}{7} & 0 & -\\frac{20}{7} & 0 & \\frac{19}{7} & -\\frac{1}{7} & 0 & \\frac{29900}{7} \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{7} & 0 & -\\frac{6}{7} & 1 & \\frac{5}{7} & -\\frac{8}{7} & 0 & \\frac{6800}{7} \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & 0 & -\\frac{4}{7} & 1 & -\\frac{4}{7} & 0 & -\\frac{6}{7} & -\\frac{24}{7} & 0 & \\frac{23200}{7} \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 300 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & \\frac{1}{7} & 0 & -\\frac{6}{7} & 0 & \\frac{5}{7} & -\\frac{8}{7} & 0 & \\frac{8200}{7} \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 400 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 500 \\\\\n", "{\\color{green}{s}}_{8} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{7} & 0 & -\\frac{6}{7} & 0 & \\frac{5}{7} & -\\frac{8}{7} & 1 & -\\frac{4}{7} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & 0 & -\\frac{1200}{7} & 0 & -\\frac{5050}{7} & 0 & -\\frac{1100}{7} & -\\frac{4400}{7} & 0 & \\frac{22475000}{7}\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 -6/7 0 -20/7 0 19/7 -1/7 0| 29900/7]\n", "[ s5| 0 0 0 0 0 1/7 0 -6/7 1 5/7 -8/7 0| 6800/7]\n", "[ s3| 0 0 0 0 0 -4/7 1 -4/7 0 -6/7 -24/7 0| 23200/7]\n", "[ x1| 1 0 0 0 0 0 0 1 0 0 0 0| 300]\n", "[ x2| 0 1 0 0 0 1/7 0 -6/7 0 5/7 -8/7 0| 8200/7]\n", "[ x3| 0 0 1 0 0 0 0 0 0 -1 0 0| 400]\n", "[ x4| 0 0 0 1 0 0 0 0 0 0 1 0| 500]\n", "[ s8| 0 0 0 0 0 1/7 0 -6/7 0 5/7 -8/7 1| -4/7]\n", "[----------+-----------------------------------------------------------------------------------------------------------------------------------+----------]\n", "[ Z| 0 0 0 0 0 -1200/7 0 -5050/7 0 -1100/7 -4400/7 0|22475000/7]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "v=matrix(QQ,1,nv,[0,-1,0,0,0,0,0,0,0,0,0]) ; R=-1172\n", "añadeRes(v,R)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[ NO NO NO NO NO NO NO 841.67 NO NO 550.00 NO]" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cocientesD(8)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "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 & -\\frac{7}{8} & 0 & -\\frac{11}{4} & 0 & \\frac{21}{8} & 0 & -\\frac{1}{8} & \\frac{8543}{2} \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & -1 & 972 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & 0 & -1 & 1 & 2 & 0 & -3 & 0 & -3 & 3316 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 300 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 1172 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 400 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & \\frac{1}{8} & 0 & -\\frac{3}{4} & 0 & \\frac{5}{8} & 0 & \\frac{7}{8} & \\frac{999}{2} \\\\\n", "{\\color{green}{s}}_{7} & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{8} & 0 & \\frac{3}{4} & 0 & -\\frac{5}{8} & 1 & -\\frac{7}{8} & \\frac{1}{2} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & 0 & -250 & 0 & -250 & 0 & -550 & 0 & -550 & 3210400\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 & -\\frac{7}{8} & 0 & -\\frac{11}{4} & 0 & \\frac{21}{8} & 0 & -\\frac{1}{8} & \\frac{8543}{2} \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & -1 & 972 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & 0 & -1 & 1 & 2 & 0 & -3 & 0 & -3 & 3316 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 300 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 1172 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 400 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & \\frac{1}{8} & 0 & -\\frac{3}{4} & 0 & \\frac{5}{8} & 0 & \\frac{7}{8} & \\frac{999}{2} \\\\\n", "{\\color{green}{s}}_{7} & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{8} & 0 & \\frac{3}{4} & 0 & -\\frac{5}{8} & 1 & -\\frac{7}{8} & \\frac{1}{2} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & 0 & -250 & 0 & -250 & 0 & -550 & 0 & -550 & 3210400\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 -7/8 0 -11/4 0 21/8 0 -1/8| 8543/2]\n", "[ s5| 0 0 0 0 0 0 0 0 1 0 0 -1| 972]\n", "[ s3| 0 0 0 0 0 -1 1 2 0 -3 0 -3| 3316]\n", "[ x1| 1 0 0 0 0 0 0 1 0 0 0 0| 300]\n", "[ x2| 0 1 0 0 0 0 0 0 0 0 0 -1| 1172]\n", "[ x3| 0 0 1 0 0 0 0 0 0 -1 0 0| 400]\n", "[ x4| 0 0 0 1 0 1/8 0 -3/4 0 5/8 0 7/8| 999/2]\n", "[ s7| 0 0 0 0 0 -1/8 0 3/4 0 -5/8 1 -7/8| 1/2]\n", "[-------+-----------------------------------------------------------------------------------------------+-------]\n", "[ Z| 0 0 0 0 0 -250 0 -250 0 -550 0 -550|3210400]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(8,11)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "########################################\n", "\n", "Añadimos $x_2 \\leq 499$" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrr|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{green}{s}}_{9} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 0 & 0 & 0 & 1 & -\\frac{7}{8} & 0 & -\\frac{11}{4} & 0 & \\frac{21}{8} & 0 & -\\frac{1}{8} & 0 & \\frac{8543}{2} \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & -1 & 0 & 972 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & 0 & -1 & 1 & 2 & 0 & -3 & 0 & -3 & 0 & 3316 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 300 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 1172 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 400 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & \\frac{1}{8} & 0 & -\\frac{3}{4} & 0 & \\frac{5}{8} & 0 & \\frac{7}{8} & 0 & \\frac{999}{2} \\\\\n", "{\\color{green}{s}}_{7} & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{8} & 0 & \\frac{3}{4} & 0 & -\\frac{5}{8} & 1 & -\\frac{7}{8} & 0 & \\frac{1}{2} \\\\\n", "{\\color{green}{s}}_{9} & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{8} & 0 & \\frac{3}{4} & 0 & -\\frac{5}{8} & 0 & -\\frac{7}{8} & 1 & -\\frac{1}{2} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & 0 & -250 & 0 & -250 & 0 & -550 & 0 & -550 & 0 & 3210400\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrr|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{green}{s}}_{9} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 0 & 0 & 0 & 1 & -\\frac{7}{8} & 0 & -\\frac{11}{4} & 0 & \\frac{21}{8} & 0 & -\\frac{1}{8} & 0 & \\frac{8543}{2} \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & -1 & 0 & 972 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & 0 & -1 & 1 & 2 & 0 & -3 & 0 & -3 & 0 & 3316 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 300 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 1172 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 400 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & \\frac{1}{8} & 0 & -\\frac{3}{4} & 0 & \\frac{5}{8} & 0 & \\frac{7}{8} & 0 & \\frac{999}{2} \\\\\n", "{\\color{green}{s}}_{7} & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{8} & 0 & \\frac{3}{4} & 0 & -\\frac{5}{8} & 1 & -\\frac{7}{8} & 0 & \\frac{1}{2} \\\\\n", "{\\color{green}{s}}_{9} & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{8} & 0 & \\frac{3}{4} & 0 & -\\frac{5}{8} & 0 & -\\frac{7}{8} & 1 & -\\frac{1}{2} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & 0 & -250 & 0 & -250 & 0 & -550 & 0 & -550 & 0 & 3210400\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7 s8 s9| rhs]\n", "[-------+-------------------------------------------------------------------------------------------------------+-------]\n", "[ s1| 0 0 0 0 1 -7/8 0 -11/4 0 21/8 0 -1/8 0| 8543/2]\n", "[ s5| 0 0 0 0 0 0 0 0 1 0 0 -1 0| 972]\n", "[ s3| 0 0 0 0 0 -1 1 2 0 -3 0 -3 0| 3316]\n", "[ x1| 1 0 0 0 0 0 0 1 0 0 0 0 0| 300]\n", "[ x2| 0 1 0 0 0 0 0 0 0 0 0 -1 0| 1172]\n", "[ x3| 0 0 1 0 0 0 0 0 0 -1 0 0 0| 400]\n", "[ x4| 0 0 0 1 0 1/8 0 -3/4 0 5/8 0 7/8 0| 999/2]\n", "[ s7| 0 0 0 0 0 -1/8 0 3/4 0 -5/8 1 -7/8 0| 1/2]\n", "[ s9| 0 0 0 0 0 -1/8 0 3/4 0 -5/8 0 -7/8 1| -1/2]\n", "[-------+-------------------------------------------------------------------------------------------------------+-------]\n", "[ Z| 0 0 0 0 0 -250 0 -250 0 -550 0 -550 0|3210400]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "v=matrix(QQ,1,nv,[0,0,0,1,0,0,0,0,0,0,0,0]) ; R=499\n", "añadeRes(v,R)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[ NO NO NO NO NO 2000.0 NO NO NO 880.00 NO 628.57 NO]" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cocientesD(9)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrr|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{green}{s}}_{9} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 0 & 0 & 0 & 1 & -\\frac{6}{7} & 0 & -\\frac{20}{7} & 0 & \\frac{19}{7} & 0 & 0 & -\\frac{1}{7} & \\frac{29901}{7} \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{7} & 0 & -\\frac{6}{7} & 1 & \\frac{5}{7} & 0 & 0 & -\\frac{8}{7} & \\frac{6808}{7} \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & 0 & -\\frac{4}{7} & 1 & -\\frac{4}{7} & 0 & -\\frac{6}{7} & 0 & 0 & -\\frac{24}{7} & \\frac{23224}{7} \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 300 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & \\frac{1}{7} & 0 & -\\frac{6}{7} & 0 & \\frac{5}{7} & 0 & 0 & -\\frac{8}{7} & \\frac{8208}{7} \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 400 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 499 \\\\\n", "{\\color{green}{s}}_{7} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & -1 & 1 \\\\\n", "{\\color{green}{s}}_{8} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{7} & 0 & -\\frac{6}{7} & 0 & \\frac{5}{7} & 0 & 1 & -\\frac{8}{7} & \\frac{4}{7} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & 0 & -\\frac{1200}{7} & 0 & -\\frac{5050}{7} & 0 & -\\frac{1100}{7} & 0 & 0 & -\\frac{4400}{7} & \\frac{22470600}{7}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrr|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{green}{s}}_{9} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 0 & 0 & 0 & 1 & -\\frac{6}{7} & 0 & -\\frac{20}{7} & 0 & \\frac{19}{7} & 0 & 0 & -\\frac{1}{7} & \\frac{29901}{7} \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{7} & 0 & -\\frac{6}{7} & 1 & \\frac{5}{7} & 0 & 0 & -\\frac{8}{7} & \\frac{6808}{7} \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & 0 & -\\frac{4}{7} & 1 & -\\frac{4}{7} & 0 & -\\frac{6}{7} & 0 & 0 & -\\frac{24}{7} & \\frac{23224}{7} \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 300 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & \\frac{1}{7} & 0 & -\\frac{6}{7} & 0 & \\frac{5}{7} & 0 & 0 & -\\frac{8}{7} & \\frac{8208}{7} \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 400 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 499 \\\\\n", "{\\color{green}{s}}_{7} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & -1 & 1 \\\\\n", "{\\color{green}{s}}_{8} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{7} & 0 & -\\frac{6}{7} & 0 & \\frac{5}{7} & 0 & 1 & -\\frac{8}{7} & \\frac{4}{7} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & 0 & -\\frac{1200}{7} & 0 & -\\frac{5050}{7} & 0 & -\\frac{1100}{7} & 0 & 0 & -\\frac{4400}{7} & \\frac{22470600}{7}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7 s8 s9| rhs]\n", "[----------+----------------------------------------------------------------------------------------------------------------------------------------------+----------]\n", "[ s1| 0 0 0 0 1 -6/7 0 -20/7 0 19/7 0 0 -1/7| 29901/7]\n", "[ s5| 0 0 0 0 0 1/7 0 -6/7 1 5/7 0 0 -8/7| 6808/7]\n", "[ s3| 0 0 0 0 0 -4/7 1 -4/7 0 -6/7 0 0 -24/7| 23224/7]\n", "[ x1| 1 0 0 0 0 0 0 1 0 0 0 0 0| 300]\n", "[ x2| 0 1 0 0 0 1/7 0 -6/7 0 5/7 0 0 -8/7| 8208/7]\n", "[ x3| 0 0 1 0 0 0 0 0 0 -1 0 0 0| 400]\n", "[ x4| 0 0 0 1 0 0 0 0 0 0 0 0 1| 499]\n", "[ s7| 0 0 0 0 0 0 0 0 0 0 1 0 -1| 1]\n", "[ s8| 0 0 0 0 0 1/7 0 -6/7 0 5/7 0 1 -8/7| 4/7]\n", "[----------+----------------------------------------------------------------------------------------------------------------------------------------------+----------]\n", "[ Z| 0 0 0 0 0 -1200/7 0 -5050/7 0 -1100/7 0 0 -4400/7|22470600/7]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(9,12)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "########################################\n", "\n", "Añadimos $x_2 \\geq 1173$" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrrr|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{green}{s}}_{9} & {\\color{green}{s}}_{10} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 0 & 0 & 0 & 1 & -\\frac{6}{7} & 0 & -\\frac{20}{7} & 0 & \\frac{19}{7} & 0 & 0 & -\\frac{1}{7} & 0 & \\frac{29901}{7} \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{7} & 0 & -\\frac{6}{7} & 1 & \\frac{5}{7} & 0 & 0 & -\\frac{8}{7} & 0 & \\frac{6808}{7} \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & 0 & -\\frac{4}{7} & 1 & -\\frac{4}{7} & 0 & -\\frac{6}{7} & 0 & 0 & -\\frac{24}{7} & 0 & \\frac{23224}{7} \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 300 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & \\frac{1}{7} & 0 & -\\frac{6}{7} & 0 & \\frac{5}{7} & 0 & 0 & -\\frac{8}{7} & 0 & \\frac{8208}{7} \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 400 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 499 \\\\\n", "{\\color{green}{s}}_{7} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & -1 & 0 & 1 \\\\\n", "{\\color{green}{s}}_{8} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{7} & 0 & -\\frac{6}{7} & 0 & \\frac{5}{7} & 0 & 1 & -\\frac{8}{7} & 0 & \\frac{4}{7} \\\\\n", "{\\color{green}{s}}_{10} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{7} & 0 & -\\frac{6}{7} & 0 & \\frac{5}{7} & 0 & 0 & -\\frac{8}{7} & 1 & -\\frac{3}{7} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & 0 & -\\frac{1200}{7} & 0 & -\\frac{5050}{7} & 0 & -\\frac{1100}{7} & 0 & 0 & -\\frac{4400}{7} & 0 & \\frac{22470600}{7}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrrr|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{green}{s}}_{9} & {\\color{green}{s}}_{10} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 0 & 0 & 0 & 1 & -\\frac{6}{7} & 0 & -\\frac{20}{7} & 0 & \\frac{19}{7} & 0 & 0 & -\\frac{1}{7} & 0 & \\frac{29901}{7} \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{7} & 0 & -\\frac{6}{7} & 1 & \\frac{5}{7} & 0 & 0 & -\\frac{8}{7} & 0 & \\frac{6808}{7} \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & 0 & -\\frac{4}{7} & 1 & -\\frac{4}{7} & 0 & -\\frac{6}{7} & 0 & 0 & -\\frac{24}{7} & 0 & \\frac{23224}{7} \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 300 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & \\frac{1}{7} & 0 & -\\frac{6}{7} & 0 & \\frac{5}{7} & 0 & 0 & -\\frac{8}{7} & 0 & \\frac{8208}{7} \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 400 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 499 \\\\\n", "{\\color{green}{s}}_{7} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & -1 & 0 & 1 \\\\\n", "{\\color{green}{s}}_{8} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{7} & 0 & -\\frac{6}{7} & 0 & \\frac{5}{7} & 0 & 1 & -\\frac{8}{7} & 0 & \\frac{4}{7} \\\\\n", "{\\color{green}{s}}_{10} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{7} & 0 & -\\frac{6}{7} & 0 & \\frac{5}{7} & 0 & 0 & -\\frac{8}{7} & 1 & -\\frac{3}{7} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & 0 & -\\frac{1200}{7} & 0 & -\\frac{5050}{7} & 0 & -\\frac{1100}{7} & 0 & 0 & -\\frac{4400}{7} & 0 & \\frac{22470600}{7}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7 s8 s9 s10| rhs]\n", "[----------+---------------------------------------------------------------------------------------------------------------------------------------------------------+----------]\n", "[ s1| 0 0 0 0 1 -6/7 0 -20/7 0 19/7 0 0 -1/7 0| 29901/7]\n", "[ s5| 0 0 0 0 0 1/7 0 -6/7 1 5/7 0 0 -8/7 0| 6808/7]\n", "[ s3| 0 0 0 0 0 -4/7 1 -4/7 0 -6/7 0 0 -24/7 0| 23224/7]\n", "[ x1| 1 0 0 0 0 0 0 1 0 0 0 0 0 0| 300]\n", "[ x2| 0 1 0 0 0 1/7 0 -6/7 0 5/7 0 0 -8/7 0| 8208/7]\n", "[ x3| 0 0 1 0 0 0 0 0 0 -1 0 0 0 0| 400]\n", "[ x4| 0 0 0 1 0 0 0 0 0 0 0 0 1 0| 499]\n", "[ s7| 0 0 0 0 0 0 0 0 0 0 1 0 -1 0| 1]\n", "[ s8| 0 0 0 0 0 1/7 0 -6/7 0 5/7 0 1 -8/7 0| 4/7]\n", "[ s10| 0 0 0 0 0 1/7 0 -6/7 0 5/7 0 0 -8/7 1| -3/7]\n", "[----------+---------------------------------------------------------------------------------------------------------------------------------------------------------+----------]\n", "[ Z| 0 0 0 0 0 -1200/7 0 -5050/7 0 -1100/7 0 0 -4400/7 0|22470600/7]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "v=matrix(QQ,1,nv,[0,-1,0,0,0,0,0,0,0,0,0,0,0]) ; R=-1173\n", "añadeRes(v,R)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrrr|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{green}{s}}_{9} & {\\color{green}{s}}_{10} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 0 & 0 & 0 & 1 & -\\frac{7}{8} & 0 & -\\frac{11}{4} & 0 & \\frac{21}{8} & 0 & 0 & 0 & -\\frac{1}{8} & \\frac{34173}{8} \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & -1 & 973 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & 0 & -1 & 1 & 2 & 0 & -3 & 0 & 0 & 0 & -3 & 3319 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 300 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 1173 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 400 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & \\frac{1}{8} & 0 & -\\frac{3}{4} & 0 & \\frac{5}{8} & 0 & 0 & 0 & \\frac{7}{8} & \\frac{3989}{8} \\\\\n", "{\\color{green}{s}}_{7} & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{8} & 0 & \\frac{3}{4} & 0 & -\\frac{5}{8} & 1 & 0 & 0 & -\\frac{7}{8} & \\frac{11}{8} \\\\\n", "{\\color{green}{s}}_{8} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & -1 & 1 \\\\\n", "{\\color{green}{s}}_{9} & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{8} & 0 & \\frac{3}{4} & 0 & -\\frac{5}{8} & 0 & 0 & 1 & -\\frac{7}{8} & \\frac{3}{8} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & 0 & -250 & 0 & -250 & 0 & -550 & 0 & 0 & 0 & -550 & 3209850\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrrr|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{green}{s}}_{9} & {\\color{green}{s}}_{10} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 0 & 0 & 0 & 1 & -\\frac{7}{8} & 0 & -\\frac{11}{4} & 0 & \\frac{21}{8} & 0 & 0 & 0 & -\\frac{1}{8} & \\frac{34173}{8} \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & -1 & 973 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & 0 & -1 & 1 & 2 & 0 & -3 & 0 & 0 & 0 & -3 & 3319 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 300 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 1173 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 400 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & \\frac{1}{8} & 0 & -\\frac{3}{4} & 0 & \\frac{5}{8} & 0 & 0 & 0 & \\frac{7}{8} & \\frac{3989}{8} \\\\\n", "{\\color{green}{s}}_{7} & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{8} & 0 & \\frac{3}{4} & 0 & -\\frac{5}{8} & 1 & 0 & 0 & -\\frac{7}{8} & \\frac{11}{8} \\\\\n", "{\\color{green}{s}}_{8} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & -1 & 1 \\\\\n", "{\\color{green}{s}}_{9} & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{8} & 0 & \\frac{3}{4} & 0 & -\\frac{5}{8} & 0 & 0 & 1 & -\\frac{7}{8} & \\frac{3}{8} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & 0 & -250 & 0 & -250 & 0 & -550 & 0 & 0 & 0 & -550 & 3209850\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7 s8 s9 s10| rhs]\n", "[-------+---------------------------------------------------------------------------------------------------------------+-------]\n", "[ s1| 0 0 0 0 1 -7/8 0 -11/4 0 21/8 0 0 0 -1/8|34173/8]\n", "[ s5| 0 0 0 0 0 0 0 0 1 0 0 0 0 -1| 973]\n", "[ s3| 0 0 0 0 0 -1 1 2 0 -3 0 0 0 -3| 3319]\n", "[ x1| 1 0 0 0 0 0 0 1 0 0 0 0 0 0| 300]\n", "[ x2| 0 1 0 0 0 0 0 0 0 0 0 0 0 -1| 1173]\n", "[ x3| 0 0 1 0 0 0 0 0 0 -1 0 0 0 0| 400]\n", "[ x4| 0 0 0 1 0 1/8 0 -3/4 0 5/8 0 0 0 7/8| 3989/8]\n", "[ s7| 0 0 0 0 0 -1/8 0 3/4 0 -5/8 1 0 0 -7/8| 11/8]\n", "[ s8| 0 0 0 0 0 0 0 0 0 0 0 1 0 -1| 1]\n", "[ s9| 0 0 0 0 0 -1/8 0 3/4 0 -5/8 0 0 1 -7/8| 3/8]\n", "[-------+---------------------------------------------------------------------------------------------------------------+-------]\n", "[ Z| 0 0 0 0 0 -250 0 -250 0 -550 0 0 0 -550|3209850]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(10,13)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "########################################\n", "\n", "Añadimos $x_4 \\leq 498$ (P7)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrrrr|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{green}{s}}_{9} & {\\color{green}{s}}_{10} & {\\color{green}{s}}_{11} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 0 & 0 & 0 & 1 & -\\frac{7}{8} & 0 & -\\frac{11}{4} & 0 & \\frac{21}{8} & 0 & 0 & 0 & -\\frac{1}{8} & 0 & \\frac{34173}{8} \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & -1 & 0 & 973 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & 0 & -1 & 1 & 2 & 0 & -3 & 0 & 0 & 0 & -3 & 0 & 3319 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 300 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 1173 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 400 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & \\frac{1}{8} & 0 & -\\frac{3}{4} & 0 & \\frac{5}{8} & 0 & 0 & 0 & \\frac{7}{8} & 0 & \\frac{3989}{8} \\\\\n", "{\\color{green}{s}}_{7} & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{8} & 0 & \\frac{3}{4} & 0 & -\\frac{5}{8} & 1 & 0 & 0 & -\\frac{7}{8} & 0 & \\frac{11}{8} \\\\\n", "{\\color{green}{s}}_{8} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & -1 & 0 & 1 \\\\\n", "{\\color{green}{s}}_{9} & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{8} & 0 & \\frac{3}{4} & 0 & -\\frac{5}{8} & 0 & 0 & 1 & -\\frac{7}{8} & 0 & \\frac{3}{8} \\\\\n", "{\\color{green}{s}}_{11} & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{8} & 0 & \\frac{3}{4} & 0 & -\\frac{5}{8} & 0 & 0 & 0 & -\\frac{7}{8} & 1 & -\\frac{5}{8} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & 0 & -250 & 0 & -250 & 0 & -550 & 0 & 0 & 0 & -550 & 0 & 3209850\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrrrr|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{green}{s}}_{9} & {\\color{green}{s}}_{10} & {\\color{green}{s}}_{11} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 0 & 0 & 0 & 1 & -\\frac{7}{8} & 0 & -\\frac{11}{4} & 0 & \\frac{21}{8} & 0 & 0 & 0 & -\\frac{1}{8} & 0 & \\frac{34173}{8} \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & -1 & 0 & 973 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & 0 & -1 & 1 & 2 & 0 & -3 & 0 & 0 & 0 & -3 & 0 & 3319 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 300 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 1173 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 400 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & \\frac{1}{8} & 0 & -\\frac{3}{4} & 0 & \\frac{5}{8} & 0 & 0 & 0 & \\frac{7}{8} & 0 & \\frac{3989}{8} \\\\\n", "{\\color{green}{s}}_{7} & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{8} & 0 & \\frac{3}{4} & 0 & -\\frac{5}{8} & 1 & 0 & 0 & -\\frac{7}{8} & 0 & \\frac{11}{8} \\\\\n", "{\\color{green}{s}}_{8} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & -1 & 0 & 1 \\\\\n", "{\\color{green}{s}}_{9} & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{8} & 0 & \\frac{3}{4} & 0 & -\\frac{5}{8} & 0 & 0 & 1 & -\\frac{7}{8} & 0 & \\frac{3}{8} \\\\\n", "{\\color{green}{s}}_{11} & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{8} & 0 & \\frac{3}{4} & 0 & -\\frac{5}{8} & 0 & 0 & 0 & -\\frac{7}{8} & 1 & -\\frac{5}{8} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & 0 & -250 & 0 & -250 & 0 & -550 & 0 & 0 & 0 & -550 & 0 & 3209850\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7 s8 s9 s10 s11| rhs]\n", "[-------+-----------------------------------------------------------------------------------------------------------------------+-------]\n", "[ s1| 0 0 0 0 1 -7/8 0 -11/4 0 21/8 0 0 0 -1/8 0|34173/8]\n", "[ s5| 0 0 0 0 0 0 0 0 1 0 0 0 0 -1 0| 973]\n", "[ s3| 0 0 0 0 0 -1 1 2 0 -3 0 0 0 -3 0| 3319]\n", "[ x1| 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0| 300]\n", "[ x2| 0 1 0 0 0 0 0 0 0 0 0 0 0 -1 0| 1173]\n", "[ x3| 0 0 1 0 0 0 0 0 0 -1 0 0 0 0 0| 400]\n", "[ x4| 0 0 0 1 0 1/8 0 -3/4 0 5/8 0 0 0 7/8 0| 3989/8]\n", "[ s7| 0 0 0 0 0 -1/8 0 3/4 0 -5/8 1 0 0 -7/8 0| 11/8]\n", "[ s8| 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 0| 1]\n", "[ s9| 0 0 0 0 0 -1/8 0 3/4 0 -5/8 0 0 1 -7/8 0| 3/8]\n", "[ s11| 0 0 0 0 0 -1/8 0 3/4 0 -5/8 0 0 0 -7/8 1| -5/8]\n", "[-------+-----------------------------------------------------------------------------------------------------------------------+-------]\n", "[ Z| 0 0 0 0 0 -250 0 -250 0 -550 0 0 0 -550 0|3209850]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "v=matrix(QQ,1,nv,[0,0,0,1,0,0,0,0,0,0,0,0,0,0]) ; R=498\n", "añadeRes(v,R)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrrrr|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{green}{s}}_{9} & {\\color{green}{s}}_{10} & {\\color{green}{s}}_{11} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 0 & 0 & 0 & 1 & -\\frac{6}{7} & 0 & -\\frac{20}{7} & 0 & \\frac{19}{7} & 0 & 0 & 0 & 0 & -\\frac{1}{7} & \\frac{29902}{7} \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{7} & 0 & -\\frac{6}{7} & 1 & \\frac{5}{7} & 0 & 0 & 0 & 0 & -\\frac{8}{7} & \\frac{6816}{7} \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & 0 & -\\frac{4}{7} & 1 & -\\frac{4}{7} & 0 & -\\frac{6}{7} & 0 & 0 & 0 & 0 & -\\frac{24}{7} & \\frac{23248}{7} \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 300 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & \\frac{1}{7} & 0 & -\\frac{6}{7} & 0 & \\frac{5}{7} & 0 & 0 & 0 & 0 & -\\frac{8}{7} & \\frac{8216}{7} \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 400 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 498 \\\\\n", "{\\color{green}{s}}_{7} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & -1 & 2 \\\\\n", "{\\color{green}{s}}_{8} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{7} & 0 & -\\frac{6}{7} & 0 & \\frac{5}{7} & 0 & 1 & 0 & 0 & -\\frac{8}{7} & \\frac{12}{7} \\\\\n", "{\\color{green}{s}}_{9} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & -1 & 1 \\\\\n", "{\\color{green}{s}}_{10} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{7} & 0 & -\\frac{6}{7} & 0 & \\frac{5}{7} & 0 & 0 & 0 & 1 & -\\frac{8}{7} & \\frac{5}{7} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & 0 & -\\frac{1200}{7} & 0 & -\\frac{5050}{7} & 0 & -\\frac{1100}{7} & 0 & 0 & 0 & 0 & -\\frac{4400}{7} & \\frac{22466200}{7}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrrrr|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{green}{s}}_{9} & {\\color{green}{s}}_{10} & {\\color{green}{s}}_{11} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 0 & 0 & 0 & 1 & -\\frac{6}{7} & 0 & -\\frac{20}{7} & 0 & \\frac{19}{7} & 0 & 0 & 0 & 0 & -\\frac{1}{7} & \\frac{29902}{7} \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{7} & 0 & -\\frac{6}{7} & 1 & \\frac{5}{7} & 0 & 0 & 0 & 0 & -\\frac{8}{7} & \\frac{6816}{7} \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & 0 & -\\frac{4}{7} & 1 & -\\frac{4}{7} & 0 & -\\frac{6}{7} & 0 & 0 & 0 & 0 & -\\frac{24}{7} & \\frac{23248}{7} \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 300 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & \\frac{1}{7} & 0 & -\\frac{6}{7} & 0 & \\frac{5}{7} & 0 & 0 & 0 & 0 & -\\frac{8}{7} & \\frac{8216}{7} \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 400 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 498 \\\\\n", "{\\color{green}{s}}_{7} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & -1 & 2 \\\\\n", "{\\color{green}{s}}_{8} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{7} & 0 & -\\frac{6}{7} & 0 & \\frac{5}{7} & 0 & 1 & 0 & 0 & -\\frac{8}{7} & \\frac{12}{7} \\\\\n", "{\\color{green}{s}}_{9} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & -1 & 1 \\\\\n", "{\\color{green}{s}}_{10} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{7} & 0 & -\\frac{6}{7} & 0 & \\frac{5}{7} & 0 & 0 & 0 & 1 & -\\frac{8}{7} & \\frac{5}{7} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & 0 & -\\frac{1200}{7} & 0 & -\\frac{5050}{7} & 0 & -\\frac{1100}{7} & 0 & 0 & 0 & 0 & -\\frac{4400}{7} & \\frac{22466200}{7}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7 s8 s9 s10 s11| rhs]\n", "[----------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------+----------]\n", "[ s1| 0 0 0 0 1 -6/7 0 -20/7 0 19/7 0 0 0 0 -1/7| 29902/7]\n", "[ s5| 0 0 0 0 0 1/7 0 -6/7 1 5/7 0 0 0 0 -8/7| 6816/7]\n", "[ s3| 0 0 0 0 0 -4/7 1 -4/7 0 -6/7 0 0 0 0 -24/7| 23248/7]\n", "[ x1| 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0| 300]\n", "[ x2| 0 1 0 0 0 1/7 0 -6/7 0 5/7 0 0 0 0 -8/7| 8216/7]\n", "[ x3| 0 0 1 0 0 0 0 0 0 -1 0 0 0 0 0| 400]\n", "[ x4| 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1| 498]\n", "[ s7| 0 0 0 0 0 0 0 0 0 0 1 0 0 0 -1| 2]\n", "[ s8| 0 0 0 0 0 1/7 0 -6/7 0 5/7 0 1 0 0 -8/7| 12/7]\n", "[ s9| 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1| 1]\n", "[ s10| 0 0 0 0 0 1/7 0 -6/7 0 5/7 0 0 0 1 -8/7| 5/7]\n", "[----------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------+----------]\n", "[ Z| 0 0 0 0 0 -1200/7 0 -5050/7 0 -1100/7 0 0 0 0 -4400/7|22466200/7]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(11,14)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "########################################\n", "\n", "Añadimos $x_2 \\leq 1173$ (P9)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\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{green}{s}}_{9} & {\\color{green}{s}}_{10} & {\\color{green}{s}}_{11} & {\\color{green}{s}}_{12} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 0 & 0 & 0 & 1 & -\\frac{6}{7} & 0 & -\\frac{20}{7} & 0 & \\frac{19}{7} & 0 & 0 & 0 & 0 & -\\frac{1}{7} & 0 & \\frac{29902}{7} \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{7} & 0 & -\\frac{6}{7} & 1 & \\frac{5}{7} & 0 & 0 & 0 & 0 & -\\frac{8}{7} & 0 & \\frac{6816}{7} \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & 0 & -\\frac{4}{7} & 1 & -\\frac{4}{7} & 0 & -\\frac{6}{7} & 0 & 0 & 0 & 0 & -\\frac{24}{7} & 0 & \\frac{23248}{7} \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 300 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & \\frac{1}{7} & 0 & -\\frac{6}{7} & 0 & \\frac{5}{7} & 0 & 0 & 0 & 0 & -\\frac{8}{7} & 0 & \\frac{8216}{7} \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 400 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 498 \\\\\n", "{\\color{green}{s}}_{7} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & -1 & 0 & 2 \\\\\n", "{\\color{green}{s}}_{8} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{7} & 0 & -\\frac{6}{7} & 0 & \\frac{5}{7} & 0 & 1 & 0 & 0 & -\\frac{8}{7} & 0 & \\frac{12}{7} \\\\\n", "{\\color{green}{s}}_{9} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & -1 & 0 & 1 \\\\\n", "{\\color{green}{s}}_{10} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{7} & 0 & -\\frac{6}{7} & 0 & \\frac{5}{7} & 0 & 0 & 0 & 1 & -\\frac{8}{7} & 0 & \\frac{5}{7} \\\\\n", "{\\color{green}{s}}_{12} & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{7} & 0 & \\frac{6}{7} & 0 & -\\frac{5}{7} & 0 & 0 & 0 & 0 & \\frac{8}{7} & 1 & -\\frac{5}{7} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & 0 & -\\frac{1200}{7} & 0 & -\\frac{5050}{7} & 0 & -\\frac{1100}{7} & 0 & 0 & 0 & 0 & -\\frac{4400}{7} & 0 & \\frac{22466200}{7}\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{green}{s}}_{9} & {\\color{green}{s}}_{10} & {\\color{green}{s}}_{11} & {\\color{green}{s}}_{12} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 0 & 0 & 0 & 1 & -\\frac{6}{7} & 0 & -\\frac{20}{7} & 0 & \\frac{19}{7} & 0 & 0 & 0 & 0 & -\\frac{1}{7} & 0 & \\frac{29902}{7} \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{7} & 0 & -\\frac{6}{7} & 1 & \\frac{5}{7} & 0 & 0 & 0 & 0 & -\\frac{8}{7} & 0 & \\frac{6816}{7} \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & 0 & -\\frac{4}{7} & 1 & -\\frac{4}{7} & 0 & -\\frac{6}{7} & 0 & 0 & 0 & 0 & -\\frac{24}{7} & 0 & \\frac{23248}{7} \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 300 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & \\frac{1}{7} & 0 & -\\frac{6}{7} & 0 & \\frac{5}{7} & 0 & 0 & 0 & 0 & -\\frac{8}{7} & 0 & \\frac{8216}{7} \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 400 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 498 \\\\\n", "{\\color{green}{s}}_{7} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & -1 & 0 & 2 \\\\\n", "{\\color{green}{s}}_{8} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{7} & 0 & -\\frac{6}{7} & 0 & \\frac{5}{7} & 0 & 1 & 0 & 0 & -\\frac{8}{7} & 0 & \\frac{12}{7} \\\\\n", "{\\color{green}{s}}_{9} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & -1 & 0 & 1 \\\\\n", "{\\color{green}{s}}_{10} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{7} & 0 & -\\frac{6}{7} & 0 & \\frac{5}{7} & 0 & 0 & 0 & 1 & -\\frac{8}{7} & 0 & \\frac{5}{7} \\\\\n", "{\\color{green}{s}}_{12} & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{7} & 0 & \\frac{6}{7} & 0 & -\\frac{5}{7} & 0 & 0 & 0 & 0 & \\frac{8}{7} & 1 & -\\frac{5}{7} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & 0 & -\\frac{1200}{7} & 0 & -\\frac{5050}{7} & 0 & -\\frac{1100}{7} & 0 & 0 & 0 & 0 & -\\frac{4400}{7} & 0 & \\frac{22466200}{7}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7 s8 s9 s10 s11 s12| rhs]\n", "[----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+----------]\n", "[ s1| 0 0 0 0 1 -6/7 0 -20/7 0 19/7 0 0 0 0 -1/7 0| 29902/7]\n", "[ s5| 0 0 0 0 0 1/7 0 -6/7 1 5/7 0 0 0 0 -8/7 0| 6816/7]\n", "[ s3| 0 0 0 0 0 -4/7 1 -4/7 0 -6/7 0 0 0 0 -24/7 0| 23248/7]\n", "[ x1| 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0| 300]\n", "[ x2| 0 1 0 0 0 1/7 0 -6/7 0 5/7 0 0 0 0 -8/7 0| 8216/7]\n", "[ x3| 0 0 1 0 0 0 0 0 0 -1 0 0 0 0 0 0| 400]\n", "[ x4| 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0| 498]\n", "[ s7| 0 0 0 0 0 0 0 0 0 0 1 0 0 0 -1 0| 2]\n", "[ s8| 0 0 0 0 0 1/7 0 -6/7 0 5/7 0 1 0 0 -8/7 0| 12/7]\n", "[ s9| 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 0| 1]\n", "[ s10| 0 0 0 0 0 1/7 0 -6/7 0 5/7 0 0 0 1 -8/7 0| 5/7]\n", "[ s12| 0 0 0 0 0 -1/7 0 6/7 0 -5/7 0 0 0 0 8/7 1| -5/7]\n", "[----------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+----------]\n", "[ Z| 0 0 0 0 0 -1200/7 0 -5050/7 0 -1100/7 0 0 0 0 -4400/7 0|22466200/7]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "v=matrix(QQ,1,nv,[0,1,0,0,0,0,0,0,0,0,0,0,0,0,0]) ; R=1173\n", "añadeRes(v,R)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\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{green}{s}}_{9} & {\\color{green}{s}}_{10} & {\\color{green}{s}}_{11} & {\\color{green}{s}}_{12} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 0 & 0 & 0 & 1 & -\\frac{7}{5} & 0 & \\frac{2}{5} & 0 & 0 & 0 & 0 & 0 & 0 & \\frac{21}{5} & \\frac{19}{5} & 4269 \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 973 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & 0 & -\\frac{2}{5} & 1 & -\\frac{8}{5} & 0 & 0 & 0 & 0 & 0 & 0 & -\\frac{24}{5} & -\\frac{6}{5} & 3322 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 300 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1173 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & \\frac{1}{5} & 0 & -\\frac{6}{5} & 0 & 0 & 0 & 0 & 0 & 0 & -\\frac{8}{5} & -\\frac{7}{5} & 401 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 498 \\\\\n", "{\\color{green}{s}}_{7} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & -1 & 0 & 2 \\\\\n", "{\\color{green}{s}}_{8} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 1 \\\\\n", "{\\color{green}{s}}_{9} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & -1 & 0 & 1 \\\\\n", "{\\color{green}{s}}_{10} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\\\\n", "{\\color{green}{s}}_{6} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{5} & 0 & -\\frac{6}{5} & 0 & 1 & 0 & 0 & 0 & 0 & -\\frac{8}{5} & -\\frac{7}{5} & 1 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & 0 & -140 & 0 & -910 & 0 & 0 & 0 & 0 & 0 & 0 & -880 & -220 & 3209300\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{green}{s}}_{9} & {\\color{green}{s}}_{10} & {\\color{green}{s}}_{11} & {\\color{green}{s}}_{12} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 0 & 0 & 0 & 1 & -\\frac{7}{5} & 0 & \\frac{2}{5} & 0 & 0 & 0 & 0 & 0 & 0 & \\frac{21}{5} & \\frac{19}{5} & 4269 \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 973 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 0 & 0 & -\\frac{2}{5} & 1 & -\\frac{8}{5} & 0 & 0 & 0 & 0 & 0 & 0 & -\\frac{24}{5} & -\\frac{6}{5} & 3322 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 300 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1173 \\\\\n", "{x}_{3} & 0 & 0 & 1 & 0 & 0 & \\frac{1}{5} & 0 & -\\frac{6}{5} & 0 & 0 & 0 & 0 & 0 & 0 & -\\frac{8}{5} & -\\frac{7}{5} & 401 \\\\\n", "{x}_{4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 498 \\\\\n", "{\\color{green}{s}}_{7} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & -1 & 0 & 2 \\\\\n", "{\\color{green}{s}}_{8} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 1 \\\\\n", "{\\color{green}{s}}_{9} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & -1 & 0 & 1 \\\\\n", "{\\color{green}{s}}_{10} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\\\\n", "{\\color{green}{s}}_{6} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{5} & 0 & -\\frac{6}{5} & 0 & 1 & 0 & 0 & 0 & 0 & -\\frac{8}{5} & -\\frac{7}{5} & 1 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & 0 & -140 & 0 & -910 & 0 & 0 & 0 & 0 & 0 & 0 & -880 & -220 & 3209300\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7 s8 s9 s10 s11 s12| rhs]\n", "[-------+-------------------------------------------------------------------------------------------------------------------------------+-------]\n", "[ s1| 0 0 0 0 1 -7/5 0 2/5 0 0 0 0 0 0 21/5 19/5| 4269]\n", "[ s5| 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1| 973]\n", "[ s3| 0 0 0 0 0 -2/5 1 -8/5 0 0 0 0 0 0 -24/5 -6/5| 3322]\n", "[ x1| 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0| 300]\n", "[ x2| 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1| 1173]\n", "[ x3| 0 0 1 0 0 1/5 0 -6/5 0 0 0 0 0 0 -8/5 -7/5| 401]\n", "[ x4| 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0| 498]\n", "[ s7| 0 0 0 0 0 0 0 0 0 0 1 0 0 0 -1 0| 2]\n", "[ s8| 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1| 1]\n", "[ s9| 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 0| 1]\n", "[ s10| 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1| 0]\n", "[ s6| 0 0 0 0 0 1/5 0 -6/5 0 1 0 0 0 0 -8/5 -7/5| 1]\n", "[-------+-------------------------------------------------------------------------------------------------------------------------------+-------]\n", "[ Z| 0 0 0 0 0 -140 0 -910 0 0 0 0 0 0 -880 -220|3209300]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(12,10)" ] } ], "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 }