{ "cells": [ { "cell_type": "code", "execution_count": 12, "metadata": { "scrolled": false }, "outputs": [ { "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}{lcrcrcrcl}\n", " \\min \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 3 x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{2} \\mspace{-6mu}&\\mspace{-6mu} + 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"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": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {b} \\\\\n", "\\hline\n", " {\\color{red}{t}}_{1} & 1 & 5 & -2 & 1 & 0 & 10 \\\\\n", "{\\color{red}{t}}_{2} & 3 & 2 & -1 & 0 & 1 & 15 \\\\\n", "\\hline\n", " {W_{ind}} & -4 & -7 & 3 & 0 & 0 & 25\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {b} \\\\\n", "\\hline\n", " {\\color{red}{t}}_{1} & 1 & 5 & -2 & 1 & 0 & 10 \\\\\n", "{\\color{red}{t}}_{2} & 3 & 2 & -1 & 0 & 1 & 15 \\\\\n", "\\hline\n", " {W_{ind}} & -4 & -7 & 3 & 0 & 0 & 25\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 t1 t2|rhs]\n", "[---+-------------------+---]\n", "[ t1| 1 5 -2 1 0| 10]\n", "[ t2| 3 2 -1 0 1| 15]\n", "[---+-------------------+---]\n", "[ W| -4 -7 3 0 0| 25]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tipo='min' # Problema de tipo max o min\n", "\n", "n=3 # número de variables x's\n", "m=2 # número de restricciones (distintas de las de signo)\n", "\n", "c=matrix(QQ,1,n,[3,1,2] ) # vector de costos\n", "\n", "A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n", "[1,5,-2],\n", "[3,2,-1]\n", "])\n", "\n", "b=matrix(QQ,m,1,[10,15]) # vector de la derecha\n", "\n", "\n", "h=matrix(ZZ,1,m,[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,[1,1]) # 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) # 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": 10, "metadata": { "scrolled": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {b} \\\\\n", "\\hline\n", " {x}_{2} & \\frac{1}{5} & 1 & -\\frac{2}{5} & \\frac{1}{5} & 0 & 0 \\\\\n", "{\\color{red}{t}}_{2} & \\frac{13}{5} & 0 & -\\frac{1}{5} & -\\frac{2}{5} & 1 & 0 \\\\\n", "\\hline\n", " 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