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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": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n", "\\begin{array}{lcrcrcrcrcl}\n", " \\max \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 250 x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 225 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 275 x_{3} \\mspace{-6mu}&\\mspace{-6mu} + 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$\\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": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{red}{t}}_{4} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 4 & 3 & 4 & 3 & 1 & 0 & 0 & 0 & 0 & 400 \\\\\n", "{\\color{green}{s}}_{2} & 5 & 4 & 5 & 4 & 0 & 1 & 0 & 0 & 0 & 500 \\\\\n", "{\\color{green}{s}}_{3} & 2 & 3 & 3 & 2 & 0 & 0 & 1 & 0 & 0 & 300 \\\\\n", "{\\color{red}{t}}_{4} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 1 & 15 \\\\\n", "\\hline\n", " {W_{ind}} & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 15\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{red}{t}}_{4} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 4 & 3 & 4 & 3 & 1 & 0 & 0 & 0 & 0 & 400 \\\\\n", "{\\color{green}{s}}_{2} & 5 & 4 & 5 & 4 & 0 & 1 & 0 & 0 & 0 & 500 \\\\\n", "{\\color{green}{s}}_{3} & 2 & 3 & 3 & 2 & 0 & 0 & 1 & 0 & 0 & 300 \\\\\n", "{\\color{red}{t}}_{4} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 1 & 15 \\\\\n", "\\hline\n", " {W_{ind}} & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 15\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 t4|rhs]\n", "[---+-----------------------------------+---]\n", "[ s1| 4 3 4 3 1 0 0 0 0|400]\n", "[ s2| 5 4 5 4 0 1 0 0 0|500]\n", "[ s3| 2 3 3 2 0 0 1 0 0|300]\n", "[ t4| 1 0 0 0 0 0 0 -1 1| 15]\n", "[---+-----------------------------------+---]\n", "[ W| -1 0 0 0 0 0 0 1 0| 15]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 4 , 1 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{red}{t}}_{4} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 3 & 4 & 3 & 1 & 0 & 0 & 4 & -4 & 340 \\\\\n", "{\\color{green}{s}}_{2} & 0 & 4 & 5 & 4 & 0 & 1 & 0 & 5 & -5 & 425 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 3 & 3 & 2 & 0 & 0 & 1 & 2 & -2 & 270 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 1 & 15 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{red}{t}}_{4} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 3 & 4 & 3 & 1 & 0 & 0 & 4 & -4 & 340 \\\\\n", "{\\color{green}{s}}_{2} & 0 & 4 & 5 & 4 & 0 & 1 & 0 & 5 & -5 & 425 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 3 & 3 & 2 & 0 & 0 & 1 & 2 & -2 & 270 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 1 & 15 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 t4|rhs]\n", "[---+-----------------------------------+---]\n", "[ s1| 0 3 4 3 1 0 0 4 -4|340]\n", "[ s2| 0 4 5 4 0 1 0 5 -5|425]\n", "[ s3| 0 3 3 2 0 0 1 2 -2|270]\n", "[ x1| 1 0 0 0 0 0 0 -1 1| 15]\n", "[---+-----------------------------------+---]\n", "[ W| 0 0 0 0 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": [ " 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"{\\color{green}{s}}_{2} & 0 & 4 & 5 & 4 & 0 & 1 & 0 & 5 & 425 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 3 & 3 & 2 & 0 & 0 & 1 & 2 & 270 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 15 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 225 & 275 & 230 & 0 & 0 & 0 & 250 & 3750\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4| rhs]\n", "[----+---------------------------------------+----]\n", "[ s1| 0 3 4 3 1 0 0 4| 340]\n", "[ s2| 0 4 5 4 0 1 0 5| 425]\n", "[ s3| 0 3 3 2 0 0 1 2| 270]\n", "[ x1| 1 0 0 0 0 0 0 -1| 15]\n", "[----+---------------------------------------+----]\n", "[ Z| 0 225 275 230 0 0 0 250|3750]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 1 , 3 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} \\\\\n", "\\hline\n", " {x}_{3} & 0 & \\frac{3}{4} & 1 & \\frac{3}{4} & \\frac{1}{4} & 0 & 0 & 1 & 85 \\\\\n", "{\\color{green}{s}}_{2} & 0 & \\frac{1}{4} & 0 & \\frac{1}{4} & -\\frac{5}{4} & 1 & 0 & 0 & 0 \\\\\n", "{\\color{green}{s}}_{3} & 0 & \\frac{3}{4} & 0 & -\\frac{1}{4} & -\\frac{3}{4} & 0 & 1 & -1 & 15 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 15 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & \\frac{75}{4} & 0 & \\frac{95}{4} & -\\frac{275}{4} & 0 & 0 & -25 & 27125\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} \\\\\n", "\\hline\n", " {x}_{3} & 0 & \\frac{3}{4} & 1 & \\frac{3}{4} & \\frac{1}{4} & 0 & 0 & 1 & 85 \\\\\n", "{\\color{green}{s}}_{2} & 0 & \\frac{1}{4} & 0 & \\frac{1}{4} & -\\frac{5}{4} & 1 & 0 & 0 & 0 \\\\\n", "{\\color{green}{s}}_{3} & 0 & \\frac{3}{4} & 0 & -\\frac{1}{4} & -\\frac{3}{4} & 0 & 1 & -1 & 15 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 15 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & \\frac{75}{4} & 0 & \\frac{95}{4} & -\\frac{275}{4} & 0 & 0 & -25 & 27125\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4| rhs]\n", "[------+-------------------------------------------------------+------]\n", "[ x3| 0 3/4 1 3/4 1/4 0 0 1| 85]\n", "[ s2| 0 1/4 0 1/4 -5/4 1 0 0| 0]\n", "[ s3| 0 3/4 0 -1/4 -3/4 0 1 -1| 15]\n", "[ x1| 1 0 0 0 0 0 0 -1| 15]\n", "[------+-------------------------------------------------------+------]\n", "[ Z| 0 75/4 0 95/4 -275/4 0 0 -25| 27125]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 2 , 4 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} \\\\\n", "\\hline\n", " {x}_{3} & 0 & 0 & 1 & 0 & 4 & -3 & 0 & 1 & 85 \\\\\n", "{x}_{4} & 0 & 1 & 0 & 1 & -5 & 4 & 0 & 0 & 0 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 1 & 0 & 0 & -2 & 1 & 1 & -1 & 15 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 15 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & -5 & 0 & 0 & 50 & -95 & 0 & -25 & 27125\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} \\\\\n", "\\hline\n", " {x}_{3} & 0 & 0 & 1 & 0 & 4 & -3 & 0 & 1 & 85 \\\\\n", "{x}_{4} & 0 & 1 & 0 & 1 & -5 & 4 & 0 & 0 & 0 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 1 & 0 & 0 & -2 & 1 & 1 & -1 & 15 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 15 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & -5 & 0 & 0 & 50 & -95 & 0 & -25 & 27125\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4| rhs]\n", "[-----+-----------------------------------------------+-----]\n", "[ x3| 0 0 1 0 4 -3 0 1| 85]\n", "[ x4| 0 1 0 1 -5 4 0 0| 0]\n", "[ s3| 0 1 0 0 -2 1 1 -1| 15]\n", "[ x1| 1 0 0 0 0 0 0 -1| 15]\n", "[-----+-----------------------------------------------+-----]\n", "[ Z| 0 -5 0 0 50 -95 0 -25|27125]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 1 , 5 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 0 & \\frac{1}{4} & 0 & 1 & -\\frac{3}{4} & 0 & \\frac{1}{4} & \\frac{85}{4} \\\\\n", "{x}_{4} & 0 & 1 & \\frac{5}{4} & 1 & 0 & \\frac{1}{4} & 0 & \\frac{5}{4} & \\frac{425}{4} \\\\\n", "{\\color{green}{s}}_{3} & 0 & 1 & \\frac{1}{2} & 0 & 0 & -\\frac{1}{2} & 1 & -\\frac{1}{2} & \\frac{115}{2} \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 15 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & -5 & -\\frac{25}{2} & 0 & 0 & -\\frac{115}{2} & 0 & -\\frac{75}{2} & \\frac{56375}{2}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 0 & \\frac{1}{4} & 0 & 1 & -\\frac{3}{4} & 0 & \\frac{1}{4} & \\frac{85}{4} \\\\\n", "{x}_{4} & 0 & 1 & \\frac{5}{4} & 1 & 0 & \\frac{1}{4} & 0 & \\frac{5}{4} & \\frac{425}{4} \\\\\n", "{\\color{green}{s}}_{3} & 0 & 1 & \\frac{1}{2} & 0 & 0 & -\\frac{1}{2} & 1 & -\\frac{1}{2} & \\frac{115}{2} \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 15 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & -5 & -\\frac{25}{2} & 0 & 0 & -\\frac{115}{2} & 0 & -\\frac{75}{2} & \\frac{56375}{2}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4| rhs]\n", "[-------+---------------------------------------------------------------+-------]\n", "[ s1| 0 0 1/4 0 1 -3/4 0 1/4| 85/4]\n", "[ x4| 0 1 5/4 1 0 1/4 0 5/4| 425/4]\n", "[ s3| 0 1 1/2 0 0 -1/2 1 -1/2| 115/2]\n", "[ x1| 1 0 0 0 0 0 0 -1| 15]\n", "[-------+---------------------------------------------------------------+-------]\n", "[ Z| 0 -5 -25/2 0 0 -115/2 0 -75/2|56375/2]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "El problema es óptimo\n" ] } ], "source": [ "tipo='max' # max o min\n", "\n", "n=4 # número de variables x's\n", "m=4 # número de restricciones (distintas de las de signo)\n", "\n", "c=matrix(QQ,1,n,[250,225,275,230] ) # vector de costos\n", "\n", "A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n", "[4,3,4,3],\n", "[5,4,5,4],\n", "[2,3,3,2],\n", "[1,0,0,0]\n", "])\n", "\n", "b=matrix(QQ,m,1,[400,500,300,15]) # vector de la derecha\n", "\n", "\n", "######################################################\n", "############### VARIABLES DE HOLGURA ################\n", "\n", "\n", "h=matrix(ZZ,1,m,[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", "t=matrix(ZZ,1,m,[0,0 ,0,1]) # 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=(5,6,7,9) # posición de la matriz identidad\n", "\n", "\n", "####################################################################\n", "############ HASTA AQUÍ LOS DATOS ################################\n", "####################################################################\n", "\n", "load('https://sage.unex.es/501708/simplex2023Auto.sage')\n", "#load('https://sage.unex.es/501708/simplex2023AutoREVISED.sage')\n", "#load('https://sage.unex.es/501708/simplex2023CompletamenteManual.sage')\n" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrrr}\n", "0 & 1 & -\\frac{4}{3} & -\\frac{7}{3} \\\\\n", "0 & -1 & \\frac{5}{3} & \\frac{5}{3} \\\\\n", "1 & -1 & \\frac{1}{3} & \\frac{1}{3} \\\\\n", "0 & 0 & 0 & 1\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrrr}\n", "0 & 1 & -\\frac{4}{3} & -\\frac{7}{3} \\\\\n", "0 & -1 & \\frac{5}{3} & \\frac{5}{3} \\\\\n", "1 & -1 & \\frac{1}{3} & \\frac{1}{3} \\\\\n", "0 & 0 & 0 & 1\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ 0 1 -4/3 -7/3]\n", "[ 0 -1 5/3 5/3]\n", "[ 1 -1 1/3 1/3]\n", "[ 0 0 0 1]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(BM1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "Añadimos un nuevo tipo de reloj, R4, $A_4^t=(3,4,2)$ y $c_4=230$\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "\n", "\n" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrrr}\n", "0 & 1 & -\\frac{4}{3} & -\\frac{7}{3} \\\\\n", "0 & -1 & \\frac{5}{3} & \\frac{5}{3} \\\\\n", "1 & -1 & \\frac{1}{3} & \\frac{1}{3} \\\\\n", "0 & 0 & 0 & 1\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrrr}\n", "0 & 1 & -\\frac{4}{3} & -\\frac{7}{3} \\\\\n", "0 & -1 & \\frac{5}{3} & \\frac{5}{3} \\\\\n", "1 & -1 & \\frac{1}{3} & \\frac{1}{3} \\\\\n", "0 & 0 & 0 & 1\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ 0 1 -4/3 -7/3]\n", "[ 0 -1 5/3 5/3]\n", "[ 1 -1 1/3 1/3]\n", "[ 0 0 0 1]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(BM1) " ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrrr}\n", "275 & 225 & 0 & 250\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrrr}\n", "275 & 225 & 0 & 250\n", "\\end{array}\\right)$$" ], "text/plain": [ "[275 225 0 250]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(cB)" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {x}_{4} & {b} \\\\\n", "\\hline\n", " {x}_{3} & 0 & 0 & 1 & 0 & 1 & -\\frac{4}{3} & \\frac{7}{3} & \\frac{4}{3} & 65 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & -1 & \\frac{5}{3} & -\\frac{5}{3} & -\\frac{2}{3} & 25 \\\\\n", "{\\color{green}{s}}_{1} & 0 & 0 & 0 & 1 & -1 & \\frac{1}{3} & -\\frac{1}{3} & -\\frac{1}{3} & 5 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 15 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & -50 & -\\frac{25}{3} & -\\frac{50}{3} & \\frac{40}{3} & 27250\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {x}_{4} & {b} \\\\\n", "\\hline\n", " {x}_{3} & 0 & 0 & 1 & 0 & 1 & -\\frac{4}{3} & \\frac{7}{3} & \\frac{4}{3} & 65 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & -1 & \\frac{5}{3} & -\\frac{5}{3} & -\\frac{2}{3} & 25 \\\\\n", "{\\color{green}{s}}_{1} & 0 & 0 & 0 & 1 & -1 & \\frac{1}{3} & -\\frac{1}{3} & -\\frac{1}{3} & 5 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 15 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & -50 & -\\frac{25}{3} & -\\frac{50}{3} & \\frac{40}{3} & 27250\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s1 s2 s3 s4 x4| rhs]\n", "[-----+-----------------------------------------------+-----]\n", "[ x3| 0 0 1 0 1 -4/3 7/3 4/3| 65]\n", "[ x2| 0 1 0 0 -1 5/3 -5/3 -2/3| 25]\n", "[ s1| 0 0 0 1 -1 1/3 -1/3 -1/3| 5]\n", "[ x1| 1 0 0 0 0 0 -1 0| 15]\n", "[-----+-----------------------------------------------+-----]\n", "[ Z| 0 0 0 0 -50 -25/3 -50/3 40/3|27250]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "v=matrix(QQ,m,1,[3,4,2,0]); c4=230;añadeVar(v,c4)" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {x}_{4} & {b} \\\\\n", "\\hline\n", " {x}_{4} & 0 & 0 & \\frac{3}{4} & 0 & \\frac{3}{4} & -1 & \\frac{7}{4} & 1 & \\frac{195}{4} \\\\\n", "{x}_{2} & 0 & 1 & \\frac{1}{2} & 0 & -\\frac{1}{2} & 1 & -\\frac{1}{2} & 0 & \\frac{115}{2} \\\\\n", "{\\color{green}{s}}_{1} & 0 & 0 & \\frac{1}{4} & 1 & -\\frac{3}{4} & 0 & \\frac{1}{4} & 0 & \\frac{85}{4} \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 15 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & -10 & 0 & -60 & 5 & -40 & 0 & 27900\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {x}_{4} & {b} \\\\\n", "\\hline\n", " {x}_{4} & 0 & 0 & \\frac{3}{4} & 0 & \\frac{3}{4} & -1 & \\frac{7}{4} & 1 & \\frac{195}{4} \\\\\n", "{x}_{2} & 0 & 1 & \\frac{1}{2} & 0 & -\\frac{1}{2} & 1 & -\\frac{1}{2} & 0 & \\frac{115}{2} \\\\\n", "{\\color{green}{s}}_{1} & 0 & 0 & \\frac{1}{4} & 1 & -\\frac{3}{4} & 0 & \\frac{1}{4} & 0 & \\frac{85}{4} \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 15 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & -10 & 0 & -60 & 5 & -40 & 0 & 27900\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s1 s2 s3 s4 x4| rhs]\n", "[-----+-----------------------------------------------+-----]\n", "[ x4| 0 0 3/4 0 3/4 -1 7/4 1|195/4]\n", "[ x2| 0 1 1/2 0 -1/2 1 -1/2 0|115/2]\n", "[ s1| 0 0 1/4 1 -3/4 0 1/4 0| 85/4]\n", "[ x1| 1 0 0 0 0 0 -1 0| 15]\n", "[-----+-----------------------------------------------+-----]\n", "[ Z| 0 0 -10 0 -60 5 -40 0|27900]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(1,8)" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {x}_{4} & {b} \\\\\n", "\\hline\n", " {x}_{4} & 0 & 1 & \\frac{5}{4} & 0 & \\frac{1}{4} & 0 & \\frac{5}{4} & 1 & \\frac{425}{4} \\\\\n", "{\\color{green}{s}}_{3} & 0 & 1 & \\frac{1}{2} & 0 & -\\frac{1}{2} & 1 & -\\frac{1}{2} & 0 & \\frac{115}{2} \\\\\n", "{\\color{green}{s}}_{1} & 0 & 0 & \\frac{1}{4} & 1 & -\\frac{3}{4} & 0 & \\frac{1}{4} & 0 & \\frac{85}{4} \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 15 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & -5 & -\\frac{25}{2} & 0 & -\\frac{115}{2} & 0 & -\\frac{75}{2} & 0 & \\frac{56375}{2}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {x}_{4} & {b} \\\\\n", "\\hline\n", " {x}_{4} & 0 & 1 & \\frac{5}{4} & 0 & \\frac{1}{4} & 0 & \\frac{5}{4} & 1 & \\frac{425}{4} \\\\\n", "{\\color{green}{s}}_{3} & 0 & 1 & \\frac{1}{2} & 0 & -\\frac{1}{2} & 1 & -\\frac{1}{2} & 0 & \\frac{115}{2} \\\\\n", "{\\color{green}{s}}_{1} & 0 & 0 & \\frac{1}{4} & 1 & -\\frac{3}{4} & 0 & \\frac{1}{4} & 0 & \\frac{85}{4} \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 15 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & -5 & -\\frac{25}{2} & 0 & -\\frac{115}{2} & 0 & -\\frac{75}{2} & 0 & \\frac{56375}{2}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s1 s2 s3 s4 x4| rhs]\n", "[-------+---------------------------------------------------------------+-------]\n", "[ x4| 0 1 5/4 0 1/4 0 5/4 1| 425/4]\n", "[ s3| 0 1 1/2 0 -1/2 1 -1/2 0| 115/2]\n", "[ s1| 0 0 1/4 1 -3/4 0 1/4 0| 85/4]\n", "[ x1| 1 0 0 0 0 0 -1 0| 15]\n", "[-------+---------------------------------------------------------------+-------]\n", "[ Z| 0 -5 -25/2 0 -115/2 0 -75/2 0|56375/2]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(2,6)" ] } ], "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 }