{ "cells": [ { "cell_type": "code", "execution_count": 21, "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": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n", "\\begin{array}{lcrcrcrcrcrcl}\n", " \\min \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 3 x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{3} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 2 x_{4} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 2 x_{5} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 3 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 4 x_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{4} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} x_{5} \\mspace{-6mu}&\\mspace{-6mu} = \\mspace{-6mu}&\\mspace{-6mu} 2 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{4} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{5} \\mspace{-6mu}&\\mspace{-6mu} = \\mspace{-6mu}&\\mspace{-6mu} 10 \\\\\n", "\\end{array} \\\\\n", "x_{1}, x_{2}, x_{3}, x_{4}, x_{5} \\geq 0\n", "\\end{array}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n", "\\begin{array}{lcrcrcrcrcrcl}\n", " \\min \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 3 x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{3} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 2 x_{4} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 2 x_{5} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 3 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 4 x_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{4} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} x_{5} \\mspace{-6mu}&\\mspace{-6mu} = \\mspace{-6mu}&\\mspace{-6mu} 2 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{4} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{5} \\mspace{-6mu}&\\mspace{-6mu} = \\mspace{-6mu}&\\mspace{-6mu} 10 \\\\\n", "\\end{array} \\\\\n", "x_{1}, x_{2}, x_{3}, x_{4}, x_{5} \\geq 0\n", "\\end{array}$$" ], "text/plain": [ "LP problem (use 'view(...)' or '%display typeset' for details)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}-20$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}-20$$" ], "text/plain": [ "-20" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(0,\\,0,\\,0,\\,6,\\,4\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(0,\\,0,\\,0,\\,6,\\,4\\right)$$" ], "text/plain": [ "(0, 0, 0, 6, 4)" ] }, "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": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {b} \\\\\n", "\\hline\n", " {\\color{red}{t}}_{1} & 1 & 3 & 4 & 1 & -1 & 1 & 0 & 2 \\\\\n", "{\\color{red}{t}}_{2} & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 10 \\\\\n", "\\hline\n", " {W_{ind}} & -2 & -4 & -5 & -2 & 0 & 0 & 0 & 12\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {b} \\\\\n", "\\hline\n", " {\\color{red}{t}}_{1} & 1 & 3 & 4 & 1 & -1 & 1 & 0 & 2 \\\\\n", "{\\color{red}{t}}_{2} & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 10 \\\\\n", "\\hline\n", " {W_{ind}} & -2 & -4 & -5 & -2 & 0 & 0 & 0 & 12\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 x5 t1 t2|rhs]\n", "[---+---------------------------+---]\n", "[ t1| 1 3 4 1 -1 1 0| 2]\n", "[ t2| 1 1 1 1 1 0 1| 10]\n", "[---+---------------------------+---]\n", "[ W| -2 -4 -5 -2 0 0 0| 12]" ] }, "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,[3,2,1,-2,-2] ) # vector de costos\n", "\n", "A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n", "[1,3,4,1,-1],\n", "[1,1,1,1,1]\n", "])\n", "\n", "b=matrix(QQ,m,1,[2,10]) # 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=(6,7) # 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": 22, "metadata": { "scrolled": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & 3 & 4 & 1 & -1 & 1 & 0 & 2 \\\\\n", "{\\color{red}{t}}_{2} & 0 & -2 & -3 & 0 & 2 & -1 & 1 & 8 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 2 & 3 & 0 & -2 & 2 & 0 & 8\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & 3 & 4 & 1 & -1 & 1 & 0 & 2 \\\\\n", "{\\color{red}{t}}_{2} & 0 & -2 & -3 & 0 & 2 & -1 & 1 & 8 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 2 & 3 & 0 & -2 & 2 & 0 & 8\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 x5 t1 t2|rhs]\n", "[---+---------------------------+---]\n", "[ x1| 1 3 4 1 -1 1 0| 2]\n", "[ t2| 0 -2 -3 0 2 -1 1| 8]\n", "[---+---------------------------+---]\n", "[ W| 0 2 3 0 -2 2 0| 8]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(1,1)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & 2 & \\frac{5}{2} & 1 & 0 & \\frac{1}{2} & \\frac{1}{2} & 6 \\\\\n", "{x}_{5} & 0 & -1 & -\\frac{3}{2} & 0 & 1 & -\\frac{1}{2} & \\frac{1}{2} & 4 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & 2 & \\frac{5}{2} & 1 & 0 & \\frac{1}{2} & \\frac{1}{2} & 6 \\\\\n", "{x}_{5} & 0 & -1 & -\\frac{3}{2} & 0 & 1 & -\\frac{1}{2} & \\frac{1}{2} & 4 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 x5 t1 t2| rhs]\n", "[----+----------------------------------+----]\n", "[ x1| 1 2 5/2 1 0 1/2 1/2| 6]\n", "[ x5| 0 -1 -3/2 0 1 -1/2 1/2| 4]\n", "[----+----------------------------------+----]\n", "[ W| 0 0 0 0 0 1 1| 0]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(2,5)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & 2 & \\frac{5}{2} & 1 & 0 & 6 \\\\\n", "{x}_{5} & 0 & -1 & -\\frac{3}{2} & 0 & 1 & 4 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & -6 & -\\frac{19}{2} & -5 & 0 & 10\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & 2 & \\frac{5}{2} & 1 & 0 & 6 \\\\\n", "{x}_{5} & 0 & -1 & -\\frac{3}{2} & 0 & 1 & 4 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & -6 & -\\frac{19}{2} & -5 & 0 & 10\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 x5| rhs]\n", "[-----+-----------------------------+-----]\n", "[ x1| 1 2 5/2 1 0| 6]\n", "[ x5| 0 -1 -3/2 0 1| 4]\n", "[-----+-----------------------------+-----]\n", "[ Z| 0 -6 -19/2 -5 0| 10]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tt=(0,0); faseII(0,tt)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "#cambio(1,2)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "scrolled": false }, "outputs": [], "source": [ "#cambio(1,3)" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {b} \\\\\n", "\\hline\n", " {x}_{4} & 1 & 2 & \\frac{5}{2} & 1 & 0 & 6 \\\\\n", "{x}_{5} & 0 & -1 & -\\frac{3}{2} & 0 & 1 & 4 \\\\\n", "\\hline\n", " {Z_{ind}} & 5 & 4 & 3 & 0 & 0 & -20\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {b} \\\\\n", "\\hline\n", " {x}_{4} & 1 & 2 & \\frac{5}{2} & 1 & 0 & 6 \\\\\n", "{x}_{5} & 0 & -1 & -\\frac{3}{2} & 0 & 1 & 4 \\\\\n", "\\hline\n", " {Z_{ind}} & 5 & 4 & 3 & 0 & 0 & -20\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 x5| rhs]\n", "[----+------------------------+----]\n", "[ x4| 1 2 5/2 1 0| 6]\n", "[ x5| 0 -1 -3/2 0 1| 4]\n", "[----+------------------------+----]\n", "[ Z| 5 4 3 0 0| -20]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(1,4)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [] } ], "metadata": { "kernelspec": { "display_name": "SageMath 9.5", "language": "sage", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.2" } }, "nbformat": 4, "nbformat_minor": 4 }