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& 0 & 0 & -\\frac{1}{2} & 0 & \\frac{2}{5} & 0 & 1 \\\\\n", "{\\color{red}{t}}_{3} & -\\frac{2}{5} & 0 & -\\frac{1}{2} & -\\frac{13}{5} & 0 & 1 & -\\frac{1}{2} & -1 & -\\frac{2}{5} & 1 & 14 \\\\\n", "\\hline\n", " {W_{ind}} & \\frac{2}{5} & 0 & \\frac{1}{2} & \\frac{13}{5} & 0 & -1 & \\frac{1}{2} & 1 & \\frac{7}{5} & 0 & 14\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 x5 x6 s1 s3 t2 t3| rhs]\n", "[-----+-----------------------------------------------------------+-----]\n", "[ x5| -1/5 0 1/2 6/5 1 0 1/2 0 -1/5 0| 2]\n", "[ x2| 2/5 1 -1/2 -7/5 0 0 -1/2 0 2/5 0| 1]\n", "[ t3| -2/5 0 -1/2 -13/5 0 1 -1/2 -1 -2/5 1| 14]\n", "[-----+-----------------------------------------------------------+-----]\n", "[ W| 2/5 0 1/2 13/5 0 -1 1/2 1 7/5 0| 14]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 3 , 6 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{3} & {\\color{red}{t}}_{2} & {\\color{red}{t}}_{3} & {b} \\\\\n", "\\hline\n", " {x}_{5} & -\\frac{1}{5} & 0 & \\frac{1}{2} & \\frac{6}{5} & 1 & 0 & \\frac{1}{2} & 0 & -\\frac{1}{5} & 0 & 2 \\\\\n", "{x}_{2} & \\frac{2}{5} & 1 & -\\frac{1}{2} & -\\frac{7}{5} & 0 & 0 & -\\frac{1}{2} & 0 & \\frac{2}{5} & 0 & 1 \\\\\n", "{x}_{6} & -\\frac{2}{5} & 0 & -\\frac{1}{2} & -\\frac{13}{5} & 0 & 1 & -\\frac{1}{2} & -1 & -\\frac{2}{5} & 1 & 14 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{3} & {\\color{red}{t}}_{2} & {\\color{red}{t}}_{3} & {b} \\\\\n", "\\hline\n", " {x}_{5} & -\\frac{1}{5} & 0 & \\frac{1}{2} & \\frac{6}{5} & 1 & 0 & \\frac{1}{2} & 0 & -\\frac{1}{5} & 0 & 2 \\\\\n", "{x}_{2} & \\frac{2}{5} & 1 & -\\frac{1}{2} & -\\frac{7}{5} & 0 & 0 & -\\frac{1}{2} & 0 & \\frac{2}{5} & 0 & 1 \\\\\n", "{x}_{6} & -\\frac{2}{5} & 0 & -\\frac{1}{2} & -\\frac{13}{5} & 0 & 1 & -\\frac{1}{2} & -1 & -\\frac{2}{5} & 1 & 14 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 x5 x6 s1 s3 t2 t3| rhs]\n", "[-----+-----------------------------------------------------------+-----]\n", "[ x5| -1/5 0 1/2 6/5 1 0 1/2 0 -1/5 0| 2]\n", "[ x2| 2/5 1 -1/2 -7/5 0 0 -1/2 0 2/5 0| 1]\n", "[ x6| -2/5 0 -1/2 -13/5 0 1 -1/2 -1 -2/5 1| 14]\n", "[-----+-----------------------------------------------------------+-----]\n", "[ W| 0 0 0 0 0 0 0 0 1 1| 0]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "El problema de la fase I es óptimo y Wopt=0. Por tanto, el original es factible\n", "Preparemos el cuadro inicial de la fase II\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\ \\ \\ Fase\\ II}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\ \\ \\ Fase\\ II}$$" ], "text/plain": [ "FII" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{3} & {b} \\\\\n", "\\hline\n", " {x}_{5} & -\\frac{1}{5} & 0 & \\frac{1}{2} & \\frac{6}{5} & 1 & 0 & \\frac{1}{2} & 0 & 2 \\\\\n", "{x}_{2} & \\frac{2}{5} & 1 & -\\frac{1}{2} & -\\frac{7}{5} & 0 & 0 & -\\frac{1}{2} & 0 & 1 \\\\\n", "{x}_{6} & -\\frac{2}{5} & 0 & -\\frac{1}{2} & -\\frac{13}{5} & 0 & 1 & -\\frac{1}{2} & -1 & 14 \\\\\n", "\\hline\n", " {Z_{ind}} & \\frac{26}{5} & 0 & 2 & \\frac{59}{5} & 0 & 0 & 0 & 4 & 67\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{3} & {b} \\\\\n", "\\hline\n", " {x}_{5} & -\\frac{1}{5} & 0 & \\frac{1}{2} & \\frac{6}{5} & 1 & 0 & \\frac{1}{2} & 0 & 2 \\\\\n", "{x}_{2} & \\frac{2}{5} & 1 & -\\frac{1}{2} & -\\frac{7}{5} & 0 & 0 & -\\frac{1}{2} & 0 & 1 \\\\\n", "{x}_{6} & -\\frac{2}{5} & 0 & -\\frac{1}{2} & -\\frac{13}{5} & 0 & 1 & -\\frac{1}{2} & -1 & 14 \\\\\n", "\\hline\n", " {Z_{ind}} & \\frac{26}{5} & 0 & 2 & \\frac{59}{5} & 0 & 0 & 0 & 4 & 67\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 x5 x6 s1 s3| rhs]\n", "[-----+-----------------------------------------------+-----]\n", "[ x5| -1/5 0 1/2 6/5 1 0 1/2 0| 2]\n", "[ x2| 2/5 1 -1/2 -7/5 0 0 -1/2 0| 1]\n", "[ x6| -2/5 0 -1/2 -13/5 0 1 -1/2 -1| 14]\n", "[-----+-----------------------------------------------+-----]\n", "[ Z| 26/5 0 2 59/5 0 0 0 4| 67]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "El problema es óptimo\n" ] } ], "source": [ "tipo ='min' # Problema de tipo max o min\n", "\n", "n=6 # número de variables x's\n", "m=3 # número de restricciones (distintas de las de signo)\n", "\n", "c=matrix(QQ,1,n,[3,1,2,6,5,4] ) # vector de costos\n", "\n", "A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n", "[0,2,1,2,4,0],\n", "[1,5,0,-1,5,0],\n", "[0,3,0,-2,4,1]\n", "])\n", "\n", "b=matrix(QQ,m,1,[10,15,25]) # vector de la derecha\n", "\n", "\n", "h=matrix(ZZ,1,m,[1,0,-1]) # variables de holgura: \n", " # Pon 1 si va sumando, \n", " # -1 si va restando y \n", " # 0 si no hay variable de holgura.\n", " \n", "\n", "\n", "\n", " \n", " \n", "####################################################################\n", "############ HASTA AQUÍ LOS DATOS ################################\n", "####################################################################\n", "\n", "\n", "load('https://sage.unex.es/501708/simplex2023Auto.sage')\n", "\n", "#load('https://sage.unex.es/501708/simplex2023CompletamenteManual.sage')" ] }, { "cell_type": "markdown", "id": "3af8c206", "metadata": {}, "source": [ "# Enredos" ] }, { "cell_type": "code", "execution_count": 3, "id": "0c0e2694", "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrr}\n", "\\frac{1}{2} & -\\frac{1}{5} & 0 \\\\\n", "-\\frac{1}{2} & \\frac{2}{5} & 0 \\\\\n", "-\\frac{1}{2} & -\\frac{2}{5} & 1\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrr}\n", "\\frac{1}{2} & -\\frac{1}{5} & 0 \\\\\n", "-\\frac{1}{2} & \\frac{2}{5} & 0 \\\\\n", "-\\frac{1}{2} & -\\frac{2}{5} & 1\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ 1/2 -1/5 0]\n", "[-1/2 2/5 0]\n", "[-1/2 -2/5 1]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(BM1)" ] }, { "cell_type": "code", "execution_count": 4, "id": "7cbd1ca7", "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|rr}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{3} & {b} & {b_1} \\\\\n", "\\hline\n", " {x}_{5} & -\\frac{1}{5} & 0 & \\frac{1}{2} & \\frac{6}{5} & 1 & 0 & \\frac{1}{2} & 0 & 2 & 1 \\\\\n", "{x}_{2} & \\frac{2}{5} & 1 & -\\frac{1}{2} & -\\frac{7}{5} & 0 & 0 & -\\frac{1}{2} & 0 & 1 & -1 \\\\\n", "{x}_{6} & -\\frac{2}{5} & 0 & -\\frac{1}{2} & -\\frac{13}{5} & 0 & 1 & -\\frac{1}{2} & -1 & 14 & -1 \\\\\n", "\\hline\n", " {Z_{ind}} & \\frac{26}{5} & 0 & 2 & \\frac{59}{5} & 0 & 0 & 0 & 4 & 67 & 0\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|rr}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{3} & {b} & {b_1} \\\\\n", "\\hline\n", " {x}_{5} & -\\frac{1}{5} & 0 & \\frac{1}{2} & \\frac{6}{5} & 1 & 0 & \\frac{1}{2} & 0 & 2 & 1 \\\\\n", "{x}_{2} & \\frac{2}{5} & 1 & -\\frac{1}{2} & -\\frac{7}{5} & 0 & 0 & -\\frac{1}{2} & 0 & 1 & -1 \\\\\n", "{x}_{6} & -\\frac{2}{5} & 0 & -\\frac{1}{2} & -\\frac{13}{5} & 0 & 1 & -\\frac{1}{2} & -1 & 14 & -1 \\\\\n", "\\hline\n", " {Z_{ind}} & \\frac{26}{5} & 0 & 2 & \\frac{59}{5} & 0 & 0 & 0 & 4 & 67 & 0\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 x5 x6 s1 s3| rhs rhs1]\n", "[-----+-----------------------------------------------+-----------]\n", "[ x5| -1/5 0 1/2 6/5 1 0 1/2 0| 2 1]\n", "[ x2| 2/5 1 -1/2 -7/5 0 0 -1/2 0| 1 -1]\n", "[ x6| -2/5 0 -1/2 -13/5 0 1 -1/2 -1| 14 -1]\n", "[-----+-----------------------------------------------+-----------]\n", "[ Z| 26/5 0 2 59/5 0 0 0 4| 67 0]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "bp=matrix(QQ,m,1,[2,0,0]); param1b(bp)" ] }, { "cell_type": "code", "execution_count": 5, "id": "90cd9870", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/usr/lib/python3/dist-packages/sage/misc/remote_file.py:46: DeprecationWarning: ssl.SSLContext() without protocol argument is deprecated.\n", " content = urlopen(req, timeout=1, context=SSLContext())\n", "/usr/lib/python3/dist-packages/sage/misc/remote_file.py:46: DeprecationWarning: ssl.PROTOCOL_TLS is deprecated\n", " content = urlopen(req, timeout=1, context=SSLContext())\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$ " ], "text/latex": [ "$$\\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}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n", "\\begin{array}{lcrcrcrcrcrcrcl}\n", " \\min \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 3 x_{1} 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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n", "\\begin{array}{lcrcrcrcrcrcrcl}\n", " \\min \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 3 x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 6 x_{4} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 5 x_{5} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 4 x_{6} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 2 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{4} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 4 x_{5} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 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-\\frac{1}{5} & 0 & 3 \\\\\n", "{x}_{2} & \\frac{2}{5} & 1 & -\\frac{1}{2} & -\\frac{7}{5} & 0 & 0 & -\\frac{1}{2} & 0 & \\frac{2}{5} & 0 & 0 \\\\\n", "{x}_{6} & -\\frac{2}{5} & 0 & -\\frac{1}{2} & -\\frac{13}{5} & 0 & 1 & -\\frac{1}{2} & -1 & -\\frac{2}{5} & 1 & 13 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{3} & {\\color{red}{t}}_{2} & {\\color{red}{t}}_{3} & {b} \\\\\n", "\\hline\n", " {x}_{5} & -\\frac{1}{5} & 0 & \\frac{1}{2} & \\frac{6}{5} & 1 & 0 & \\frac{1}{2} & 0 & -\\frac{1}{5} & 0 & 3 \\\\\n", "{x}_{2} & \\frac{2}{5} & 1 & -\\frac{1}{2} & -\\frac{7}{5} & 0 & 0 & -\\frac{1}{2} & 0 & \\frac{2}{5} & 0 & 0 \\\\\n", "{x}_{6} & -\\frac{2}{5} & 0 & -\\frac{1}{2} & -\\frac{13}{5} & 0 & 1 & -\\frac{1}{2} & -1 & -\\frac{2}{5} & 1 & 13 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 x5 x6 s1 s3 t2 t3| rhs]\n", "[-----+-----------------------------------------------------------+-----]\n", "[ x5| -1/5 0 1/2 6/5 1 0 1/2 0 -1/5 0| 3]\n", "[ x2| 2/5 1 -1/2 -7/5 0 0 -1/2 0 2/5 0| 0]\n", "[ x6| -2/5 0 -1/2 -13/5 0 1 -1/2 -1 -2/5 1| 13]\n", "[-----+-----------------------------------------------------------+-----]\n", "[ W| 0 0 0 0 0 0 0 0 1 1| 0]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "El problema de la fase I es óptimo y Wopt=0. Por tanto, el original es factible\n", "Preparemos el cuadro inicial de la fase II\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\ \\ \\ Fase\\ II}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\ \\ \\ Fase\\ II}$$" ], "text/plain": [ "FII" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{3} & {b} \\\\\n", "\\hline\n", " {x}_{5} & -\\frac{1}{5} & 0 & \\frac{1}{2} & \\frac{6}{5} & 1 & 0 & \\frac{1}{2} & 0 & 3 \\\\\n", "{x}_{2} & \\frac{2}{5} & 1 & -\\frac{1}{2} & -\\frac{7}{5} & 0 & 0 & -\\frac{1}{2} & 0 & 0 \\\\\n", "{x}_{6} & -\\frac{2}{5} & 0 & -\\frac{1}{2} & -\\frac{13}{5} & 0 & 1 & -\\frac{1}{2} & -1 & 13 \\\\\n", "\\hline\n", " {Z_{ind}} & \\frac{26}{5} & 0 & 2 & \\frac{59}{5} & 0 & 0 & 0 & 4 & 67\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{3} & {b} \\\\\n", "\\hline\n", " {x}_{5} & -\\frac{1}{5} & 0 & \\frac{1}{2} & \\frac{6}{5} & 1 & 0 & \\frac{1}{2} & 0 & 3 \\\\\n", "{x}_{2} & \\frac{2}{5} & 1 & -\\frac{1}{2} & -\\frac{7}{5} & 0 & 0 & -\\frac{1}{2} & 0 & 0 \\\\\n", "{x}_{6} & -\\frac{2}{5} & 0 & -\\frac{1}{2} & -\\frac{13}{5} & 0 & 1 & -\\frac{1}{2} & -1 & 13 \\\\\n", "\\hline\n", " {Z_{ind}} & \\frac{26}{5} & 0 & 2 & \\frac{59}{5} & 0 & 0 & 0 & 4 & 67\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 x5 x6 s1 s3| rhs]\n", "[-----+-----------------------------------------------+-----]\n", "[ x5| -1/5 0 1/2 6/5 1 0 1/2 0| 3]\n", "[ x2| 2/5 1 -1/2 -7/5 0 0 -1/2 0| 0]\n", "[ x6| -2/5 0 -1/2 -13/5 0 1 -1/2 -1| 13]\n", "[-----+-----------------------------------------------+-----]\n", "[ Z| 26/5 0 2 59/5 0 0 0 4| 67]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "El problema es óptimo\n" ] } ], "source": [ "tipo ='min' # Problema de tipo max o min\n", "\n", "n=6 # número de variables x's\n", "m=3 # número de restricciones (distintas de las de signo)\n", "\n", "c=matrix(QQ,1,n,[3,1,2,6,5,4] ) # vector de costos\n", "\n", "A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n", "[0,2,1,2,4,0],\n", "[1,5,0,-1,5,0],\n", "[0,3,0,-2,4,1]\n", "])\n", "\n", "b=matrix(QQ,m,1,[12,15,25]) # vector de la derecha\n", "\n", "\n", "h=matrix(ZZ,1,m,[1,0,-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", " \n", "####################################################################\n", "############ HASTA AQUÍ LOS DATOS ################################\n", "####################################################################\n", "\n", "\n", "load('https://sage.unex.es/501708/simplex2023Auto.sage')\n", "\n", "#load('https://sage.unex.es/501708/simplex2023CompletamenteManual.sage')" ] }, { "cell_type": "code", "execution_count": null, "id": "0bf0816e", "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 }