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"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": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{red}{t}}_{4} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 4 & 3 & 4 & 1 & 0 & 0 & 0 & 0 & 400 \\\\\n", "{\\color{green}{s}}_{2} & 5 & 4 & 5 & 0 & 1 & 0 & 0 & 0 & 500 \\\\\n", "{\\color{green}{s}}_{3} & 2 & 3 & 3 & 0 & 0 & 1 & 0 & 0 & 300 \\\\\n", "{\\color{red}{t}}_{4} & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 1 & 15 \\\\\n", "\\hline\n", " {W_{ind}} & -1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 15\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{red}{t}}_{4} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 4 & 3 & 4 & 1 & 0 & 0 & 0 & 0 & 400 \\\\\n", "{\\color{green}{s}}_{2} & 5 & 4 & 5 & 0 & 1 & 0 & 0 & 0 & 500 \\\\\n", "{\\color{green}{s}}_{3} & 2 & 3 & 3 & 0 & 0 & 1 & 0 & 0 & 300 \\\\\n", "{\\color{red}{t}}_{4} & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 1 & 15 \\\\\n", "\\hline\n", " {W_{ind}} & -1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 15\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s1 s2 s3 s4 t4|rhs]\n", "[---+-------------------------------+---]\n", "[ s1| 4 3 4 1 0 0 0 0|400]\n", "[ s2| 5 4 5 0 1 0 0 0|500]\n", "[ s3| 2 3 3 0 0 1 0 0|300]\n", "[ t4| 1 0 0 0 0 0 -1 1| 15]\n", "[---+-------------------------------+---]\n", "[ W| -1 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": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{red}{t}}_{4} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 3 & 4 & 1 & 0 & 0 & 4 & -4 & 340 \\\\\n", "{\\color{green}{s}}_{2} & 0 & 4 & 5 & 0 & 1 & 0 & 5 & -5 & 425 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 3 & 3 & 0 & 0 & 1 & 2 & -2 & 270 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 1 & 15 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{red}{t}}_{4} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 3 & 4 & 1 & 0 & 0 & 4 & -4 & 340 \\\\\n", "{\\color{green}{s}}_{2} & 0 & 4 & 5 & 0 & 1 & 0 & 5 & -5 & 425 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 3 & 3 & 0 & 0 & 1 & 2 & -2 & 270 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 1 & 15 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s1 s2 s3 s4 t4|rhs]\n", "[---+-------------------------------+---]\n", "[ s1| 0 3 4 1 0 0 4 -4|340]\n", "[ s2| 0 4 5 0 1 0 5 -5|425]\n", "[ s3| 0 3 3 0 0 1 2 -2|270]\n", "[ x1| 1 0 0 0 0 0 -1 1| 15]\n", "[---+-------------------------------+---]\n", "[ W| 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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"[-----+-----------------------------------------+-----]\n", "[ Z| 0 0 0 25 -75 0 -25|27125]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 3 , 4 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} \\\\\n", "\\hline\n", " {x}_{3} & 0 & 0 & 1 & 0 & 1 & -\\frac{4}{3} & \\frac{7}{3} & 65 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & -1 & \\frac{5}{3} & -\\frac{5}{3} & 25 \\\\\n", "{\\color{green}{s}}_{1} & 0 & 0 & 0 & 1 & -1 & \\frac{1}{3} & -\\frac{1}{3} & 5 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 15 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & -50 & -\\frac{25}{3} & -\\frac{50}{3} & 27250\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} \\\\\n", "\\hline\n", " {x}_{3} & 0 & 0 & 1 & 0 & 1 & -\\frac{4}{3} & \\frac{7}{3} & 65 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & -1 & \\frac{5}{3} & -\\frac{5}{3} & 25 \\\\\n", "{\\color{green}{s}}_{1} & 0 & 0 & 0 & 1 & -1 & \\frac{1}{3} & -\\frac{1}{3} & 5 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 15 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & -50 & -\\frac{25}{3} & -\\frac{50}{3} & 27250\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s1 s2 s3 s4| rhs]\n", "[-----+-----------------------------------------+-----]\n", "[ x3| 0 0 1 0 1 -4/3 7/3| 65]\n", "[ x2| 0 1 0 0 -1 5/3 -5/3| 25]\n", "[ s1| 0 0 0 1 -1 1/3 -1/3| 5]\n", "[ x1| 1 0 0 0 0 0 -1| 15]\n", "[-----+-----------------------------------------+-----]\n", "[ Z| 0 0 0 0 -50 -25/3 -50/3|27250]" ] }, "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=3 # 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] ) # vector de costos\n", "\n", "A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n", "[4,3,4],\n", "[5,4,5],\n", "[2,3,3],\n", "[1,0,0]\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=(4,5,6,8) # 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": 2, "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": 5, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} \\\\\n", "\\hline\n", " {x}_{3} & 0 & 0 & 1 & 0 & 1 & -\\frac{4}{3} & \\frac{7}{3} & 65 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & -1 & \\frac{5}{3} & -\\frac{5}{3} & 25 \\\\\n", "{\\color{green}{s}}_{1} & 0 & 0 & 0 & 1 & -1 & \\frac{1}{3} & -\\frac{1}{3} & 5 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 15 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & -50 & -\\frac{25}{3} & -\\frac{50}{3} & 27250 \\\\\n", "{Z{1p}} & 0 & 0 & 0 & 0 & -50 & -\\frac{25}{3} & -\\frac{50}{3} & 27250\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} \\\\\n", "\\hline\n", " {x}_{3} & 0 & 0 & 1 & 0 & 1 & -\\frac{4}{3} & \\frac{7}{3} & 65 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & -1 & \\frac{5}{3} & -\\frac{5}{3} & 25 \\\\\n", "{\\color{green}{s}}_{1} & 0 & 0 & 0 & 1 & -1 & \\frac{1}{3} & -\\frac{1}{3} & 5 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 15 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & -50 & -\\frac{25}{3} & -\\frac{50}{3} & 27250 \\\\\n", "{Z{1p}} & 0 & 0 & 0 & 0 & -50 & -\\frac{25}{3} & -\\frac{50}{3} & 27250\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s1 s2 s3 s4| rhs]\n", "[-----+-----------------------------------------+-----]\n", "[ x3| 0 0 1 0 1 -4/3 7/3| 65]\n", "[ x2| 0 1 0 0 -1 5/3 -5/3| 25]\n", "[ s1| 0 0 0 1 -1 1/3 -1/3| 5]\n", "[ x1| 1 0 0 0 0 0 -1| 15]\n", "[-----+-----------------------------------------+-----]\n", "[ Z| 0 0 0 0 -50 -25/3 -50/3|27250]\n", "[ Z1p| 0 0 0 0 -50 -25/3 -50/3|27250]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cp1=matrix(QQ,1,n,[250,225,275]); param1c(cp1)" ] } ], "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 }