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1/10 1 0 0 1| 1]\n", "[-----+-----------------------------------+-----]\n", "[ Z| 0 0 0 0 0 -1| 1]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "El problema es óptimo\n" ] } ], "source": [ "tipo='max' # Problema de tipo max o min\n", "\n", "n=3 # número de variables x's\n", "m=3 # número de restricciones (distintas de las de signo)\n", "\n", "c=matrix(QQ,1,n,[1/100,1/10,1] ) # vector de costos\n", "\n", "A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n", "[1,0,0],\n", "[1/10,1,0],\n", "[1/100, 1/10, 1]\n", "])\n", "\n", "b=matrix(QQ,m,1,[1,1,1]) # vector de la derecha\n", "\n", "\n", "h=matrix(ZZ,1,m,[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", "t=matrix(ZZ,1,m,[0,0,0]) # variables artificiales: \n", " # pon 1 si utilizas variable artificial en la fila i-ésima\n", " # 0 si no utilizas variable artificial en la fila 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"\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s1 s2 s3|rhs]\n", "[---+-----------------------+---]\n", "[ x1| 1 0 0 1 0 0| 5]\n", "[ x2| 0 1 0 -10 1 0| 5]\n", "[ x3| 0 0 1 0 -10 1| 0]\n", "[---+-----------------------+---]\n", "[ Z| 0 0 0 0 0 -1|550]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "El problema es óptimo\n" ] } ], "source": [ "tipo='max' # Problema de tipo max o min\n", "\n", "n=3 # número de variables x's\n", "m=3 # número de restricciones (distintas de las de signo)\n", "\n", "c=matrix(QQ,1,n,[100,10,1] ) # vector de costos\n", "\n", "A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n", "[1,0,0],\n", "[10,1,0],\n", "[100, 10, 1]\n", "])\n", "\n", "b=matrix(QQ,m,1,[5,55,550]) # vector de la derecha\n", "\n", "\n", "h=matrix(ZZ,1,m,[1,1,1]) # variables de holgura: \n", " # Pon 1 si va sumando, \n", " # -1 si va restando y \n", " # 0 si no hay variable de holgura.\n", " \n", "t=matrix(ZZ,1,m,[0,0,0]) # variables artificiales: \n", " # pon 1 si utilizas variable artificial en la fila i-ésima\n", " # 0 si no utilizas variable artificial en la fila i-ésima\n", "\n", "colId=(4,5,6) # posición de la matriz identidad\n", "\n", "\n", " \n", " \n", "####################################################################\n", "############ HASTA AQUÍ LOS DATOS ################################\n", "####################################################################\n", "\n", "\n", "load('https://sage.unex.es/501708/simplex2023Auto.sage')\n", "\n", "#load('https://sage.unex.es/501708/simplex2023CompletamenteManual.sage')" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": 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"output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(0,\\,0,\\,0\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(0,\\,0,\\,0\\right)$$" ], "text/plain": [ "(0, 0, 0)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{}$$" ], "text/plain": [ "salto" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\ \\ \\ Fase\\ I}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\ \\ \\ Fase\\ I}$$" ], "text/plain": [ "FI" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {\\color{red}{t}}_{3} & {b} \\\\\n", "\\hline\n", " {\\color{red}{t}}_{1} & 0 & -1 & 1 & -1 & 0 & 0 & 1 & 0 & 0 & 0 \\\\\n", "{\\color{red}{t}}_{2} & 1 & 0 & -1 & 0 & -1 & 0 & 0 & 1 & 0 & 0 \\\\\n", "{\\color{red}{t}}_{3} & -1 & 1 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0\n", "\\end{array}\\right)$ " ], 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"stdout", "output_type": "stream", "text": [ "El problema de la fase I es óptimo y Wopt=0. Por tanto, el original es factible\n", "Preparemos el cuadro inicial de la fase II\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {\\color{red}{t}}_{3} & {b} \\\\\n", "\\hline\n", " {x}_{2} & 0 & 1 & -1 & 1 & 0 & 0 & -1 & 0 & 0 & 0 \\\\\n", "{\\color{red}{t}}_{2} & 1 & 0 & -1 & 0 & -1 & 0 & 0 & 1 & 0 & 0 \\\\\n", "{\\color{red}{t}}_{3} & -1 & 0 & 1 & -1 & 0 & -1 & 1 & 0 & 1 & 0 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & 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"{x}_{1} & 1 & 0 & -1 & 0 & -1 & 0 & 0 & 1 & 0 & 0 \\\\\n", "{\\color{red}{t}}_{3} & 0 & 1 & -1 & 0 & -1 & -1 & 0 & 1 & 1 & 0 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & -1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 0\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s1 s2 s3 t1 t2 t3|rhs]\n", "[---+-----------------------------------+---]\n", "[ s1| 0 1 -1 1 0 0 -1 0 0| 0]\n", "[ x1| 1 0 -1 0 -1 0 0 1 0| 0]\n", "[ t3| 0 1 -1 0 -1 -1 0 1 1| 0]\n", "[---+-----------------------------------+---]\n", "[ W| 0 -1 1 0 1 1 1 0 0| 0]" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {\\color{red}{t}}_{3} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & -1 & 1 & 0 & 1 & 1 & 0 & -1 & -1 & 0 & 0 \\\\\n", "{x}_{3} & -1 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"tipo=\"min\"\n", "n=3 # número de variables x's\n", "m=3 # número de restricciones (distintas de las de signo)\n", "\n", "c=matrix(QQ,1,n,[0,0,0] ) # vector de costos\n", "\n", "A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n", "[0,-1,1],\n", "[1,0,-1],\n", "[-1,1,0]\n", "])\n", "\n", "\n", "\n", "b=matrix(QQ,m,1,[0,0,0]) # vector de la derecha\n", "\n", "\n", "######################################################\n", "############### VARIABLES DE HOLGURA ################\n", "\n", "\n", "h=matrix(ZZ,1,m,[-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", "load('https://sage.unex.es/501708/simplex2023Auto.sage')" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} 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