{ "cells": [ { "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": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$ " ], "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": [ 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\\mspace{-6mu}&\\mspace{-6mu} 15 \\\\\n", "\\end{array} \\\\\n", "x_{1}, x_{2}, x_{3}, x_{4}, x_{5} \\geq 0\n", "\\end{array}$$" ], "text/plain": [ "LP problem (use 'view(...)' or '%display typeset' for details)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}7$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}7$$" ], "text/plain": [ "7" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(0,\\,1,\\,0,\\,0,\\,2\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(0,\\,1,\\,0,\\,0,\\,2\\right)$$" ], "text/plain": [ "(0, 1, 0, 0, 2)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{}$$" ], "text/plain": [ "salto" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {b} \\\\\n", "\\hline\n", " {x}_{3} & 0 & 2 & 1 & 2 & 4 & 10 \\\\\n", "{x}_{1} & 1 & 5 & 0 & -1 & 5 & 15 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & -18 & 0 & -2 & -25 & 75\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {b} \\\\\n", "\\hline\n", " {x}_{3} & 0 & 2 & 1 & 2 & 4 & 10 \\\\\n", "{x}_{1} & 1 & 5 & 0 & -1 & 5 & 15 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & -18 & 0 & -2 & -25 & 75\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 x5|rhs]\n", "[---+-------------------+---]\n", "[ x3| 0 2 1 2 4| 10]\n", "[ x1| 1 5 0 -1 5| 15]\n", "[---+-------------------+---]\n", "[ Z| 0 -18 0 -2 -25| 75]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tipo='min' # Problema de tipo max o min\n", "\n", "n=5 # número de variables x's\n", "m=2 # número de restricciones (distintas de las de signo)\n", "\n", "c=matrix(QQ,1,n,[3,3,3,1,2] ) # vector de costos\n", "\n", "A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n", "[0,2,1,2,4],\n", "[1,5,0,-1,5]\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,[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=(3,1) # 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": 5, "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} & {x}_{4} & 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"[-----+-----------------------------+-----]\n", "[ Z| 0 -11/2 25/4 21/2 0| 25/2]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(1,5)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\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}_{5} & -\\frac{1}{5} & 0 & \\frac{1}{2} & \\frac{6}{5} & 1 & 2 \\\\\n", "{x}_{2} & \\frac{2}{5} & 1 & -\\frac{1}{2} & -\\frac{7}{5} & 0 & 1 \\\\\n", "\\hline\n", " {Z_{ind}} & \\frac{11}{5} & 0 & \\frac{7}{2} & \\frac{14}{5} & 0 & 7\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} & {x}_{4} & {x}_{5} & {b} \\\\\n", "\\hline\n", " {x}_{5} & -\\frac{1}{5} & 0 & \\frac{1}{2} & \\frac{6}{5} & 1 & 2 \\\\\n", "{x}_{2} & \\frac{2}{5} & 1 & 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