{ "cells": [ { "cell_type": "code", "execution_count": 12, "id": "7a01f30b", "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": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n", "\\begin{array}{lcrcrcrcrcl}\n", " \\min \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{2} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 2 x_{3} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 3 x_{4} \\mspace{-6mu}&\\mspace{-6mu} 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"text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(44,\\,0,\\,28\\right)$$" ], "text/plain": [ "(44, 0, 28)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{}$$" ], "text/plain": [ "salto" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & 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"######################################################\n", "############### VARIABLES DE HOLGURA ################\n", "\n", "\n", "h=matrix(ZZ,1,m,[-1,-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,[1,1])\n", "\n", "colId=(6,7)\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": 18, "id": "60abcb8c", "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n", "{Basic} & {x}_{1} & 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"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & -3 & 0 & -2 & -1 & 2 & 1 & 44 \\\\\n", "{x}_{3} & 0 & -2 & 1 & -1 & -1 & 1 & 1 & 28 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s1 s2 t1 t2|rhs]\n", "[---+---------------------------+---]\n", "[ x1| 1 -3 0 -2 -1 2 1| 44]\n", "[ x3| 0 -2 1 -1 -1 1 1| 28]\n", "[---+---------------------------+---]\n", "[ W| 0 0 0 0 0 1 1| 0]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(1,1)" ] }, { "cell_type": "code", "execution_count": 20, "id": "de989534", "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & -3 & 0 & -2 & -1 & 44 \\\\\n", "{x}_{3} & 0 & -2 & 1 & -1 & -1 & 28 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 1 & 1 & 28\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 s1 s2|rhs]\n", "[---+-------------------+---]\n", "[ x1| 1 -3 0 -2 -1| 44]\n", "[ x3| 0 -2 1 -1 -1| 28]\n", "[---+-------------------+---]\n", "[ Z| 0 0 0 1 1| 28]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tt=[0,0]; faseII(0,tt)" ] }, { "cell_type": "code", "execution_count": null, "id": "057a7651", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 21, "id": "241f066b", "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\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} \\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} 2 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} 9 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 3 x_{3} \\mspace{-6mu}&\\mspace{-6mu} = \\mspace{-6mu}&\\mspace{-6mu} 4 \\\\\n", "\\end{array} \\\\\n", "x_{1}, x_{2}, x_{3} \\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(\\frac{6}{7},\\,\\frac{17}{7},\\,0\\right)$$" ], "text/plain": [ "(6/7, 17/7, 0)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{}$$" ], "text/plain": [ "salto" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\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} & 2 & 3 & 4 & 1 & 0 & 9 \\\\\n", "{\\color{red}{t}}_{2} & -1 & 2 & 3 & 0 & 1 & 4 \\\\\n", "\\hline\n", " {W_{ind}} & -1 & -5 & -7 & 0 & 0 & 13\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 t1 t2|rhs]\n", "[---+-------------------+---]\n", "[ t1| 2 3 4 1 0| 9]\n", "[ t2| -1 2 3 0 1| 4]\n", "[---+-------------------+---]\n", "[ W| -1 -5 -7 0 0| 13]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tipo='min' # max o min\n", "\n", "n=3 # número de variables x's\n", "m=2 # número de restricciones (distintas de las de signo)\n", "\n", "c=matrix(QQ,1,n,[0,0,0] ) # vector de costos\n", "\n", "A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n", "[2,3,4],\n", "[-1,2,3]\n", "])\n", "\n", "b=matrix(QQ,m,1,[9,4]) # vector de la derecha\n", "\n", "\n", "######################################################\n", "############### VARIABLES DE HOLGURA ################\n", "\n", "\n", "h=matrix(ZZ,1,m,[0,0]) # variables de holgura: \n", " # Pon 1 si va sumando, \n", " # -1 si va restando y \n", " # 0 si no hay variable de holgura.\n", "t=matrix(ZZ,1,m,[1,1])\n", "\n", "colId=(4,5)\n", "\n", "\n", "\n", "\n", "\n", "####################################################################\n", "############ HASTA AQUÍ LOS DATOS ################################\n", "####################################################################\n", "\n", "\n", "\n", "load('https://sage.unex.es/501708/simplex2023CompletamenteManual.sage')\n", "\n", "#load('https://sage.unex.es/501708/simplex2023Auto.sage')" ] }, { "cell_type": "code", "execution_count": 22, "id": "8bc5cd32", "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {b} \\\\\n", "\\hline\n", " {\\color{red}{t}}_{1} & \\frac{10}{3} & \\frac{1}{3} & 0 & 1 & -\\frac{4}{3} & \\frac{11}{3} \\\\\n", "{x}_{3} & -\\frac{1}{3} & \\frac{2}{3} & 1 & 0 & \\frac{1}{3} & \\frac{4}{3} \\\\\n", "\\hline\n", " {W_{ind}} & -\\frac{10}{3} & -\\frac{1}{3} & 0 & 0 & \\frac{7}{3} & \\frac{11}{3}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 t1 t2| rhs]\n", "[-----+-----------------------------+-----]\n", "[ t1| 10/3 1/3 0 1 -4/3| 11/3]\n", "[ x3| -1/3 2/3 1 0 1/3| 4/3]\n", "[-----+-----------------------------+-----]\n", "[ W|-10/3 -1/3 0 0 7/3| 11/3]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(2,3)" ] }, { "cell_type": "code", "execution_count": 23, "id": "6af8ac5d", "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & \\frac{1}{10} & 0 & \\frac{3}{10} & -\\frac{2}{5} & \\frac{11}{10} \\\\\n", "{x}_{3} & 0 & \\frac{7}{10} & 1 & \\frac{1}{10} & \\frac{1}{5} & \\frac{17}{10} \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & 1 & 1 & 0\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 t1 t2| rhs]\n", "[-----+-----------------------------+-----]\n", "[ x1| 1 1/10 0 3/10 -2/5|11/10]\n", "[ x3| 0 7/10 1 1/10 1/5|17/10]\n", "[-----+-----------------------------+-----]\n", "[ W| 0 0 0 1 1| 0]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(1,1)" ] }, { "cell_type": "code", "execution_count": 24, "id": "ebbd22ef", "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & \\frac{1}{10} & 0 & \\frac{11}{10} \\\\\n", "{x}_{3} & 0 & \\frac{7}{10} & 1 & \\frac{17}{10} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3| rhs]\n", "[-----+-----------------+-----]\n", "[ x1| 1 1/10 0|11/10]\n", "[ x3| 0 7/10 1|17/10]\n", "[-----+-----------------+-----]\n", "[ Z| 0 0 0| 0]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tt=[0,0];faseII(0,tt)" ] }, { "cell_type": "code", "execution_count": 11, "id": "03730316", "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {b} \\\\\n", "\\hline\n", " {x}_{1} & 1 & 0 & -\\frac{1}{7} & \\frac{19}{7} \\\\\n", "{x}_{2} & 0 & 1 & \\frac{10}{7} & \\frac{27}{7} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3| rhs]\n", "[----+--------------+----]\n", "[ x1| 1 0 -1/7|19/7]\n", "[ x2| 0 1 10/7|27/7]\n", "[----+--------------+----]\n", "[ Z| 0 0 0| 0]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(2,2)" ] } ], "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" } }, 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