{ "cells": [ { "cell_type": "code", "execution_count": 115, "metadata": { "scrolled": false }, "outputs": [ { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "execution_count": 115, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from IPython.display import IFrame\n", "\n", "# Inserta el nombre del archivo PDF en la siguiente línea\n", "archivo_pdf = \"Relojes.pdf\"\n", "\n", "# Cargar el PDF\n", "IFrame(archivo_pdf, width=1000, height=1500)\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "scrolled": false }, "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": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n", "\\begin{array}{lcrcrcrcl}\n", " \\max \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 250 x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 225 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 275 x_{3} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 4 x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 3 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 4 x_{3} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 400 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 5 x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 4 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 5 x_{3} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 500 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 2 x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 3 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 3 x_{3} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 300 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} x_{1} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 15 \\\\\n", "\\end{array} \\\\\n", "x_{1}, x_{2}, x_{3} \\geq 0\n", "\\end{array}$$" ], "text/plain": [ "LP problem (use 'view(...)' or '%display typeset' for details)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}27250$$" ], "text/plain": [ "27250" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(15,\\,25,\\,65\\right)$$" ], "text/plain": [ "(15, 25, 65)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{}$$" ], "text/plain": [ "salto" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "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" } ], "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": 132, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "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" } ], "source": [ "cambio(4,1)" ] }, { "cell_type": "code", "execution_count": 133, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrrr}\n", "1 & 0 & 0 & -4 \\\\\n", "0 & 1 & 0 & -5 \\\\\n", "0 & 0 & 1 & -2 \\\\\n", "0 & 0 & 0 & 1\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ 1 0 0 -4]\n", "[ 0 1 0 -5]\n", "[ 0 0 1 -2]\n", "[ 0 0 0 1]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(BM1)" ] }, { "cell_type": "code", "execution_count": 118, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 3 & 4 & 1 & 0 & 0 & 4 & 340 \\\\\n", "{\\color{green}{s}}_{2} & 0 & 4 & 5 & 0 & 1 & 0 & 5 & 425 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 3 & 3 & 0 & 0 & 1 & 2 & 270 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 15 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 225 & 275 & 0 & 0 & 0 & 250 & 3750\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s1 s2 s3 s4| rhs]\n", "[----+----------------------------------+----]\n", "[ s1| 0 3 4 1 0 0 4| 340]\n", "[ s2| 0 4 5 0 1 0 5| 425]\n", "[ s3| 0 3 3 0 0 1 2| 270]\n", "[ x1| 1 0 0 0 0 0 -1| 15]\n", "[----+----------------------------------+----]\n", "[ Z| 0 225 275 0 0 0 250|3750]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tt=[0,0,0,0];faseII(0,tt)" ] }, { "cell_type": "code", "execution_count": 119, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[85.000]\n", "[85.000]\n", "[90.000]\n", "[ NO]" ] }, "execution_count": 119, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cocientes(3)\n" ] }, { "cell_type": "code", "execution_count": 120, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} \\\\\n", "\\hline\n", " {x}_{3} & 0 & \\frac{3}{4} & 1 & \\frac{1}{4} & 0 & 0 & 1 & 85 \\\\\n", "{\\color{green}{s}}_{2} & 0 & \\frac{1}{4} & 0 & -\\frac{5}{4} & 1 & 0 & 0 & 0 \\\\\n", "{\\color{green}{s}}_{3} & 0 & \\frac{3}{4} & 0 & -\\frac{3}{4} & 0 & 1 & -1 & 15 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 15 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & \\frac{75}{4} & 0 & -\\frac{275}{4} & 0 & 0 & -25 & 27125\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s1 s2 s3 s4| rhs]\n", "[------+------------------------------------------------+------]\n", "[ x3| 0 3/4 1 1/4 0 0 1| 85]\n", "[ s2| 0 1/4 0 -5/4 1 0 0| 0]\n", "[ s3| 0 3/4 0 -3/4 0 1 -1| 15]\n", "[ x1| 1 0 0 0 0 0 -1| 15]\n", "[------+------------------------------------------------+------]\n", "[ Z| 0 75/4 0 -275/4 0 0 -25| 27125]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(1,3)" ] }, { "cell_type": "code", "execution_count": 121, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrrr}\n", "\\frac{1}{4} & 0 & 0 & -1 \\\\\n", "-\\frac{5}{4} & 1 & 0 & 0 \\\\\n", "-\\frac{3}{4} & 0 & 1 & 1 \\\\\n", "0 & 0 & 0 & 1\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ 1/4 0 0 -1]\n", "[-5/4 1 0 0]\n", "[-3/4 0 1 1]\n", "[ 0 0 0 1]" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrrr}\n", "\\frac{1}{4} & 0 & 0 & 0 \\\\\n", "-\\frac{5}{4} & 1 & 0 & 0 \\\\\n", "-\\frac{3}{4} & 0 & 1 & 0 \\\\\n", "0 & 0 & 0 & 1\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ 1/4 0 0 0]\n", "[-5/4 1 0 0]\n", "[-3/4 0 1 0]\n", "[ 0 0 0 1]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(BM1); show(P)" ] }, { "cell_type": "code", "execution_count": 122, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} \\\\\n", "\\hline\n", " {x}_{3} & 0 & 0 & 1 & 4 & -3 & 0 & 1 & 85 \\\\\n", "{x}_{2} & 0 & 1 & 0 & -5 & 4 & 0 & 0 & 0 \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & 3 & -3 & 1 & -1 & 15 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 15 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 25 & -75 & 0 & -25 & 27125\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s1 s2 s3 s4| rhs]\n", "[-----+-----------------------------------------+-----]\n", "[ x3| 0 0 1 4 -3 0 1| 85]\n", "[ x2| 0 1 0 -5 4 0 0| 0]\n", "[ s3| 0 0 0 3 -3 1 -1| 15]\n", "[ x1| 1 0 0 0 0 0 -1| 15]\n", "[-----+-----------------------------------------+-----]\n", "[ Z| 0 0 0 25 -75 0 -25|27125]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(2,2)" ] }, { "cell_type": "code", "execution_count": 123, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrrr}\n", "4 & -3 & 0 & -1 \\\\\n", "-5 & 4 & 0 & 0 \\\\\n", "3 & -3 & 1 & 1 \\\\\n", "0 & 0 & 0 & 1\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ 4 -3 0 -1]\n", "[-5 4 0 0]\n", "[ 3 -3 1 1]\n", "[ 0 0 0 1]" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrrr}\n", "1 & -3 & 0 & 0 \\\\\n", "0 & 4 & 0 & 0 \\\\\n", "0 & -3 & 1 & 0 \\\\\n", "0 & 0 & 0 & 1\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ 1 -3 0 0]\n", "[ 0 4 0 0]\n", "[ 0 -3 1 0]\n", "[ 0 0 0 1]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(BM1);show(P)" ] }, { "cell_type": "code", "execution_count": 124, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/html": [ "" ], "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", 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"metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r}\n", "1 \\\\\n", "-1 \\\\\n", "-1 \\\\\n", "0\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ 1]\n", "[-1]\n", "[-1]\n", "[ 0]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "bp=matrix(QQ,m,1,[0,1,0,0]);bpprima=BM1*bp;show(bpprima)" ] }, { "cell_type": "code", "execution_count": 127, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r}\n", "50\n", "\\end{array}\\right)$$" ], "text/plain": [ "[50]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(cB*bpprima)" ] }, { "cell_type": "code", "execution_count": 128, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} \\\\\n", "\\hline\n", " {x}_{3} & 0 & 0 & 1 & 1 & 0 & -1 & 2 & 70 \\\\\n", "{x}_{2} & 0 & 1 & 0 & -1 & 0 & \\frac{4}{3} & -\\frac{4}{3} & 20 \\\\\n", "{\\color{green}{s}}_{2} & 0 & 0 & 0 & -1 & 1 & -\\frac{1}{3} & \\frac{1}{3} & -5 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 15 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & -50 & 0 & -25 & 0 & 27500\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s1 s2 s3 s4| rhs]\n", "[-----+-----------------------------------------+-----]\n", "[ x3| 0 0 1 1 0 -1 2| 70]\n", "[ x2| 0 1 0 -1 0 4/3 -4/3| 20]\n", "[ s2| 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 -50 0 -25 0|27500]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(3,5)" ] }, { "cell_type": "code", "execution_count": 129, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrrr}\n", "1 & 0 & -1 & -2 \\\\\n", "-1 & 0 & \\frac{4}{3} & \\frac{4}{3} \\\\\n", "-1 & 1 & -\\frac{1}{3} & -\\frac{1}{3} \\\\\n", "0 & 0 & 0 & 1\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ 1 0 -1 -2]\n", "[ -1 0 4/3 4/3]\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": 130, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r}\n", "0 \\\\\n", "0 \\\\\n", "1 \\\\\n", "0\n", "\\end{array}\\right)$$" ], "text/plain": [ "[0]\n", "[0]\n", "[1]\n", "[0]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "bpprimaprima=BM1*bp;show(bpprimaprima)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], 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