{ "cells": [ { "cell_type": "code", "execution_count": 51, "metadata": { "scrolled": true }, "outputs": [ { "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": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n", "\\begin{array}{lcrcrcrcrcrcl}\n", " \\max \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 0 \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} x_{1} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{4} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{5} \\mspace{-6mu}&\\mspace{-6mu} = \\mspace{-6mu}&\\mspace{-6mu} 15 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} x_{2} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{4} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{5} \\mspace{-6mu}&\\mspace{-6mu} = \\mspace{-6mu}&\\mspace{-6mu} 12 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} x_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{4} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 3 x_{5} \\mspace{-6mu}&\\mspace{-6mu} = \\mspace{-6mu}&\\mspace{-6mu} 0 \\\\\n", "\\end{array} \\\\\n", "x_{1}, x_{2}, x_{3}, x_{4}, x_{5} \\geq 0\n", "\\end{array}$$" ], "text/plain": [ "LP problem (use 'view(...)' or '%display typeset' for details)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}0$$" ], "text/plain": [ "0" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(15,\\,12,\\,0,\\,0,\\,0\\right)$$" ], "text/plain": [ "(15, 12, 0, 0, 0)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ 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x5|rhs]\n", "[---+-------------------+---]\n", "[ x1| 1 0 0 1 2| 15]\n", "[ x2| 0 1 0 2 1| 12]\n", "[ x3| 0 0 1 2 3| 0]\n", "[---+-------------------+---]\n", "[ Z| 0 0 0 0 0| 0]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tipo ='max' # Problema de tipo max o min\n", "\n", "n=5 # número de variables x's\n", "m=3 # número de restricciones (distintas de las de signo)\n", "\n", "c=matrix(QQ,1,n,[0,0,0,0,0] ) # vector de costos\n", "\n", "A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n", "[1,0,0,1,2],\n", "[0,1,0,2,1],\n", "[0,0,1,2,3]\n", "])\n", "\n", "b=matrix(QQ,m,1,[15,12,0]) # vector de la derecha\n", "\n", "\n", "h=matrix(ZZ,1,m,[0,0,0]) # 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=(1,2,3) # posición de la matriz identidad\n", "\n", "\n", " \n", " \n", "####################################################################\n", "############ HASTA AQUÍ LOS DATOS ################################\n", "####################################################################\n", "\n", "\n", "\n", "\n", "load('https://sage.unex.es/501708/simplex2023CompletamenteManual.sage')" ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "scrolled": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & 0 & -\\frac{1}{2} & 0 & \\frac{1}{2} & 15 \\\\\n", "{x}_{2} & 0 & 1 & -1 & 0 & -2 & 12 \\\\\n", "{x}_{4} & 0 & 0 & \\frac{1}{2} & 1 & \\frac{3}{2} & 0 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & 0 & 0\n", "\\end{array}\\right)$$" ], "text/plain": [ 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"[ x2| 0 1 -1/3 4/3 0| 12]\n", "[ x5| 0 0 1/3 2/3 1| 0]\n", "[----+------------------------+----]\n", "[ Z| 0 0 0 0 0| 0]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(3,5)" ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [ { "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": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n", "\\begin{array}{lcrcrcrcrcrcl}\n", " \\max \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 0 \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} x_{1} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{4} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 2 x_{5} \\mspace{-6mu}&\\mspace{-6mu} = \\mspace{-6mu}&\\mspace{-6mu} 5 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} x_{2} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{4} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{5} \\mspace{-6mu}&\\mspace{-6mu} = \\mspace{-6mu}&\\mspace{-6mu} 12 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} x_{3} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 2 x_{4} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 3 x_{5} \\mspace{-6mu}&\\mspace{-6mu} = \\mspace{-6mu}&\\mspace{-6mu} 0 \\\\\n", "\\end{array} \\\\\n", "x_{1}, x_{2}, x_{3}, x_{4}, x_{5} \\geq 0\n", "\\end{array}$$" ], "text/plain": [ "LP problem (use 'view(...)' or '%display typeset' for details)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}0$$" ], "text/plain": [ "0" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(5,\\,12,\\,0,\\,0,\\,0\\right)$$" 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# -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=(1,2,3) # posición de la matriz identidad\n", "\n", "\n", " \n", " \n", "####################################################################\n", "############ HASTA AQUÍ LOS DATOS ################################\n", "####################################################################\n", "\n", "\n", "\n", "\n", "load('https://sage.unex.es/501708/simplex2023CompletamenteManual.sage')" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & -\\frac{1}{2} & 0 & 0 & -\\frac{5}{2} & -1 \\\\\n", "{x}_{4} & 0 & \\frac{1}{2} & 0 & 1 & \\frac{1}{2} & 6 \\\\\n", "{x}_{3} & 0 & 1 & 1 & 0 & 4 & 12 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & 0 & 0\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 x5| rhs]\n", "[----+------------------------+----]\n", "[ x1| 1 -1/2 0 0 -5/2| -1]\n", "[ x4| 0 1/2 0 1 1/2| 6]\n", "[ x3| 0 1 1 0 4| 12]\n", "[----+------------------------+----]\n", "[ Z| 0 0 0 0 0| 0]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(2,4)" ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & \\frac{1}{8} & \\frac{5}{8} & 0 & 0 & \\frac{13}{2} \\\\\n", "{x}_{4} & 0 & \\frac{3}{8} & -\\frac{1}{8} & 1 & 0 & \\frac{9}{2} \\\\\n", "{x}_{5} & 0 & 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