{ "cells": [ { "cell_type": "code", "execution_count": 21, "id": "22a460ae", "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": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n", "\\begin{array}{lcrcrcrcl}\n", " \\min \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 5 x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{2} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} x_{3} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} - 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-1 & 1 & -1 & 0 & 1 & 8 \\\\\n", "{\\color{green}{s}}_{2} & 1 & -2 & 2 & 1 & 0 & 10 \\\\\n", "\\hline\n", " {W_{ind}} & 1 & -1 & 1 & 0 & 0 & 8\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s2 t1|rhs]\n", "[---+-------------------+---]\n", "[ t1| -1 1 -1 0 1| 8]\n", "[ s2| 1 -2 2 1 0| 10]\n", "[---+-------------------+---]\n", "[ W| 1 -1 1 0 0| 8]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tipo='min' # 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,[-5,2,-1] ) # vector de costos\n", "\n", "A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n", "[-1,1,-1],\n", "[1,-2,2]\n", "])\n", "\n", "b=matrix(QQ,m,1,[8,10]) # vector de la derecha\n", "\n", "\n", "######################################################\n", "############### VARIABLES DE HOLGURA ################\n", "\n", "\n", "h=matrix(ZZ,1,m,[0,1]) # variables de holgura: \n", " # Pon 1 si va sumando, \n", " # -1 si va restando y \n", " # 0 si no hay variable de holgura.\n", "t=matrix(ZZ,1,m,[1,0])\n", "\n", "colId=(5,4)\n", "\n", "\n", "\n", "\n", "\n", "####################################################################\n", "############ HASTA AQUÍ LOS DATOS ################################\n", "####################################################################\n", "\n", "\n", "\n", "load('https://sage.unex.es/501708/simplex2023CompletamenteManual.sage')\n", "\n", "#load('https://sage.unex.es/501708/simplex2023Auto.sage')" ] }, { "cell_type": "code", "execution_count": 22, "id": "eab3f1e2", "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{2} & {\\color{red}{t}}_{1} & {b} \\\\\n", "\\hline\n", " {x}_{2} & -1 & 1 & -1 & 0 & 1 & 8 \\\\\n", "{\\color{green}{s}}_{2} & -1 & 0 & 0 & 1 & 2 & 26 \\\\\n", 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"[ Z| -3 0 1 0| 16]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tt=[0,0]; faseII(0,tt)" ] }, { "cell_type": "code", "execution_count": 24, "id": "9c3c76b5", "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\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}{lcrcrcrcl}\n", " \\min \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 5 x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{3} 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{\\color{green}{s}}_{2} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {b} \\\\\n", "\\hline\n", " {\\color{red}{t}}_{1} & -1 & 0 & 1 & 0 & 1 & 0 & 8 \\\\\n", "{\\color{red}{t}}_{2} & 1 & -2 & 2 & -1 & 0 & 1 & 10 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 2 & -3 & 1 & 0 & 0 & 18\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s2 t1 t2|rhs]\n", "[---+-----------------------+---]\n", "[ t1| -1 0 1 0 1 0| 8]\n", "[ t2| 1 -2 2 -1 0 1| 10]\n", "[---+-----------------------+---]\n", "[ W| 0 2 -3 1 0 0| 18]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tipo='min' # max o min\n", "\n", "n=3 # número de variables x's\n", "m=2 # número de restricciones (distintas de las de signo)\n", "\n", "c=matrix(QQ,1,n,[5,2,1] ) # vector de costos\n", "\n", "A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n", "[-1,0,1],\n", "[1,-2,2]\n", "])\n", "\n", "b=matrix(QQ,m,1,[8,10]) # vector de la derecha\n", "\n", "\n", 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{x}_{3} & {\\color{green}{s}}_{2} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {b} \\\\\n", "\\hline\n", " {\\color{red}{t}}_{1} & 0 & -2 & 3 & -1 & 1 & 1 & 18 \\\\\n", "{x}_{1} & 1 & -2 & 2 & -1 & 0 & 1 & 10 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 2 & -3 & 1 & 0 & 0 & 18\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s2 t1 t2|rhs]\n", "[---+-----------------------+---]\n", "[ t1| 0 -2 3 -1 1 1| 18]\n", "[ x1| 1 -2 2 -1 0 1| 10]\n", "[---+-----------------------+---]\n", "[ W| 0 2 -3 1 0 0| 18]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(2,1)" ] }, { "cell_type": "code", "execution_count": 26, "id": "40ffe515", "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{2} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {b} \\\\\n", "\\hline\n", " 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