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$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$ " ], "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": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{red}{t}}_{2} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & -1 & 1 & -1 & 1 & 0 & 16 \\\\\n", "{\\color{red}{t}}_{2} & -1 & 2 & 2 & 0 & 1 & 12 \\\\\n", "\\hline\n", " {W_{ind}} & 1 & -2 & -2 & 0 & 0 & 12\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{red}{t}}_{2} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & -1 & 1 & -1 & 1 & 0 & 16 \\\\\n", "{\\color{red}{t}}_{2} & -1 & 2 & 2 & 0 & 1 & 12 \\\\\n", "\\hline\n", " {W_{ind}} & 1 & -2 & -2 & 0 & 0 & 12\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s1 t2|rhs]\n", "[---+-------------------+---]\n", "[ s1| -1 1 -1 1 0| 16]\n", "[ t2| -1 2 2 0 1| 12]\n", "[---+-------------------+---]\n", "[ W| 1 -2 -2 0 0| 12]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 2 , 2 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{red}{t}}_{2} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & -\\frac{1}{2} & 0 & -2 & 1 & -\\frac{1}{2} & 10 \\\\\n", "{x}_{2} & -\\frac{1}{2} & 1 & 1 & 0 & \\frac{1}{2} & 6 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & 0 & 1 & 0\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{red}{t}}_{2} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & -\\frac{1}{2} & 0 & -2 & 1 & -\\frac{1}{2} & 10 \\\\\n", "{x}_{2} & -\\frac{1}{2} & 1 & 1 & 0 & \\frac{1}{2} & 6 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & 0 & 1 & 0\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s1 t2| rhs]\n", "[----+------------------------+----]\n", "[ s1|-1/2 0 -2 1 -1/2| 10]\n", "[ x2|-1/2 1 1 0 1/2| 6]\n", "[----+------------------------+----]\n", "[ W| 0 0 0 0 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": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & -\\frac{1}{2} & 0 & -2 & 1 & 10 \\\\\n", "{x}_{2} & -\\frac{1}{2} & 1 & 1 & 0 & 6 \\\\\n", "\\hline\n", " {Z_{ind}} & -4 & 0 & -3 & 0 & 12\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & -\\frac{1}{2} & 0 & -2 & 1 & 10 \\\\\n", "{x}_{2} & -\\frac{1}{2} & 1 & 1 & 0 & 6 \\\\\n", "\\hline\n", " {Z_{ind}} & -4 & 0 & -3 & 0 & 12\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s1| rhs]\n", "[----+-------------------+----]\n", "[ s1|-1/2 0 -2 1| 10]\n", "[ x2|-1/2 1 1 0| 6]\n", "[----+-------------------+----]\n", "[ Z| -4 0 -3 0| 12]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "El problema es no acotado\n" ] } ], "source": [ "tipo='min' # max o min\n", "\n", "n=3 # número de variables x's\n", "m=2 # número de restricciones (distintas de las de signo)\n", "\n", "c=matrix(QQ,1,n,[-5,2,-1] ) # vector de costos\n", "\n", "A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n", "[-1,1,-1],\n", "[-1,2,2]\n", "])\n", "\n", "b=matrix(QQ,m,1,[16,12]) # vector de la derecha\n", "\n", "\n", "######################################################\n", "############### VARIABLES DE HOLGURA ################\n", "\n", "\n", "h=matrix(ZZ,1,m,[1,0]) # 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", "####################################################################\n", "############ HASTA AQUÍ LOS DATOS ################################\n", "####################################################################\n", "\n", "\n", "\n", "load('https://sage.unex.es/501708/simplex2023Auto.sage')" ] }, { "cell_type": "code", "execution_count": null, "id": "f49efdd3", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 9, "id": "9c3c76b5", "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": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n", "\\begin{array}{lcrcrcrcl}\n", " \\min 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"\\end{array}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n", "\\begin{array}{lcrcrcl}\n", " \\max \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 6 y_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 12 y_{2} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} y_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{2} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 5 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 y_{2} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 2 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} y_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 y_{2} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} -1 \\\\\n", "\\end{array} \\\\\n", "y_{1} \\leq 0\n", "\\end{array}$$" ], "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": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}-6$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}-6$$" ], "text/plain": [ "-6" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(0,\\,-\\frac{1}{2}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(0,\\,-\\frac{1}{2}\\right)$$" ], "text/plain": [ "(0, -1/2)" ] }, "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": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{red}{t}}_{2} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & -1 & 1 & -1 & 1 & 0 & 6 \\\\\n", "{\\color{red}{t}}_{2} & 1 & 2 & 2 & 0 & 1 & 12 \\\\\n", "\\hline\n", " {W_{ind}} & -1 & -2 & -2 & 0 & 0 & 12\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{red}{t}}_{2} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & -1 & 1 & -1 & 1 & 0 & 6 \\\\\n", "{\\color{red}{t}}_{2} & 1 & 2 & 2 & 0 & 1 & 12 \\\\\n", "\\hline\n", " {W_{ind}} & -1 & -2 & -2 & 0 & 0 & 12\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s1 t2|rhs]\n", "[---+-------------------+---]\n", "[ s1| -1 1 -1 1 0| 6]\n", "[ t2| 1 2 2 0 1| 12]\n", "[---+-------------------+---]\n", "[ W| -1 -2 -2 0 0| 12]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 1 , 2 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{red}{t}}_{2} & {b} \\\\\n", "\\hline\n", " {x}_{2} & -1 & 1 & -1 & 1 & 0 & 6 \\\\\n", "{\\color{red}{t}}_{2} & 3 & 0 & 4 & -2 & 1 & 0 \\\\\n", "\\hline\n", " {W_{ind}} & -3 & 0 & -4 & 2 & 0 & 0\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{red}{t}}_{2} & {b} \\\\\n", "\\hline\n", " {x}_{2} & -1 & 1 & -1 & 1 & 0 & 6 \\\\\n", "{\\color{red}{t}}_{2} & 3 & 0 & 4 & -2 & 1 & 0 \\\\\n", "\\hline\n", " {W_{ind}} & -3 & 0 & -4 & 2 & 0 & 0\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s1 t2|rhs]\n", "[---+-------------------+---]\n", "[ x2| -1 1 -1 1 0| 6]\n", "[ t2| 3 0 4 -2 1| 0]\n", "[---+-------------------+---]\n", "[ W| -3 0 -4 2 0| 0]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 2 , 3 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{red}{t}}_{2} & {b} \\\\\n", "\\hline\n", " {x}_{2} & -\\frac{1}{4} & 1 & 0 & \\frac{1}{2} & \\frac{1}{4} & 6 \\\\\n", "{x}_{3} & \\frac{3}{4} & 0 & 1 & -\\frac{1}{2} & \\frac{1}{4} & 0 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & 0 & 1 & 0\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{red}{t}}_{2} & {b} \\\\\n", "\\hline\n", " {x}_{2} & -\\frac{1}{4} & 1 & 0 & \\frac{1}{2} & \\frac{1}{4} & 6 \\\\\n", "{x}_{3} & \\frac{3}{4} & 0 & 1 & -\\frac{1}{2} & \\frac{1}{4} & 0 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & 0 & 1 & 0\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s1 t2| rhs]\n", "[----+------------------------+----]\n", "[ x2|-1/4 1 0 1/2 1/4| 6]\n", "[ x3| 3/4 0 1 -1/2 1/4| 0]\n", "[----+------------------------+----]\n", "[ W| 0 0 0 0 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": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {b} \\\\\n", "\\hline\n", " {x}_{2} & -\\frac{1}{4} & 1 & 0 & \\frac{1}{2} & 6 \\\\\n", "{x}_{3} & \\frac{3}{4} & 0 & 1 & -\\frac{1}{2} & 0 \\\\\n", "\\hline\n", " {Z_{ind}} & \\frac{25}{4} & 0 & 0 & -\\frac{3}{2} & 12\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {b} \\\\\n", "\\hline\n", " {x}_{2} & -\\frac{1}{4} & 1 & 0 & \\frac{1}{2} & 6 \\\\\n", "{x}_{3} & \\frac{3}{4} & 0 & 1 & -\\frac{1}{2} & 0 \\\\\n", "\\hline\n", " {Z_{ind}} & \\frac{25}{4} & 0 & 0 & -\\frac{3}{2} & 12\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s1| rhs]\n", "[----+-------------------+----]\n", "[ x2|-1/4 1 0 1/2| 6]\n", "[ x3| 3/4 0 1 -1/2| 0]\n", "[----+-------------------+----]\n", "[ Z|25/4 0 0 -3/2| 12]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 1 , 4 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & -\\frac{1}{2} & 2 & 0 & 1 & 12 \\\\\n", "{x}_{3} & \\frac{1}{2} & 1 & 1 & 0 & 6 \\\\\n", "\\hline\n", " {Z_{ind}} & \\frac{11}{2} & 3 & 0 & 0 & -6\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & -\\frac{1}{2} & 2 & 0 & 1 & 12 \\\\\n", "{x}_{3} & \\frac{1}{2} & 1 & 1 & 0 & 6 \\\\\n", "\\hline\n", " {Z_{ind}} & \\frac{11}{2} & 3 & 0 & 0 & -6\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s1| rhs]\n", "[----+-------------------+----]\n", "[ s1|-1/2 2 0 1| 12]\n", "[ x3| 1/2 1 1 0| 6]\n", "[----+-------------------+----]\n", "[ Z|11/2 3 0 0| -6]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "El problema es óptimo\n" ] } ], "source": [ "tipo='min' # max o min\n", "\n", "n=3 # número de variables x's\n", "m=2 # número de restricciones (distintas de las de signo)\n", "\n", "c=matrix(QQ,1,n,[5,2,-1] ) # vector de costos\n", "\n", "A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n", "[-1,1,-1],\n", "[1,2,2]\n", "])\n", "\n", "b=matrix(QQ,m,1,[6,12]) # vector de la derecha\n", "\n", "\n", "######################################################\n", "############### VARIABLES DE HOLGURA ################\n", "\n", "\n", "h=matrix(ZZ,1,m,[1,0]) # 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", "####################################################################\n", "############ HASTA AQUÍ LOS DATOS ################################\n", "####################################################################\n", "\n", "\n", "\n", "load('https://sage.unex.es/501708/simplex2023Auto.sage')" ] }, { "cell_type": "code", "execution_count": null, "id": "70775953", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "d1e43dfb", "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": 5 }