{ "cells": [ { "cell_type": "code", "execution_count": 16, "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": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\ \\ \\ Fase\\ I}$$" ], "text/plain": [ "FI" ] }, "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": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {\\color{red}{t}}_{3} & {\\color{red}{t}}_{4} & {b} \\\\\n", "\\hline\n", " {\\color{red}{t}}_{1} & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 6 \\\\\n", "{\\color{red}{t}}_{2} & 1 & 1 & 0 & 3 & 2 & 1 & 0 & 1 & 0 & 0 & 8 \\\\\n", "{\\color{red}{t}}_{3} & 1 & 2 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 6 \\\\\n", "{\\color{red}{t}}_{4} & 3 & 4 & 2 & 5 & 4 & 2 & 0 & 0 & 0 & 1 & 20 \\\\\n", "\\hline\n", " {W_{ind}} & -6 & -8 & -4 & -10 & -8 & -4 & 0 & 0 & 0 & 0 & 40\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 x5 x6 t1 t2 t3 t4|rhs]\n", "[---+---------------------------------------+---]\n", "[ t1| 1 1 1 1 1 1 1 0 0 0| 6]\n", "[ t2| 1 1 0 3 2 1 0 1 0 0| 8]\n", "[ t3| 1 2 1 1 1 0 0 0 1 0| 6]\n", "[ t4| 3 4 2 5 4 2 0 0 0 1| 20]\n", "[---+---------------------------------------+---]\n", "[ W| -6 -8 -4 -10 -8 -4 0 0 0 0| 40]" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}4$$" ], "text/plain": [ "4" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tipo='max' # max o min\n", "\n", "n=6 # número de variables x's\n", "m=4 # número de restricciones (distintas de las de signo)\n", "\n", "c=matrix(QQ,1,n,[10,14,12,18,20,16] ) # vector de costos\n", "\n", "A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n", "[1,1,1,1,1,1],\n", "[1,1,0,3,2,1],\n", "[1,2,1,1,1,0],\n", "[3,4,2,5,4,2]\n", "])\n", "\n", "b=matrix(QQ,m,1,[6,8,6,20]) # vector de la derecha\n", "\n", "\n", "######################################################\n", "############### VARIABLES DE HOLGURA ################\n", "\n", "\n", "h=matrix(ZZ,1,m,[0,0,0,0]) # 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", "\n", "\n", "####################################################################\n", "############ HASTA AQUÍ LOS DATOS ################################\n", "####################################################################\n", "\n", "\n", "\n", "\n", "\n", "load('https://sage.unex.es/501708/simplex2023ManualRevisada.sage')\n" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rr|rr}\n", "{Basic} & {b} & {Col\\ Entr} & {Cocientes} \\\\\n", "{\\color{red}{t}}_{1} & 6 & 1 & 6.0000 \\\\\n", "{\\color{red}{t}}_{2} & 8 & 3 & 2.6667 \\\\\n", "{\\color{red}{t}}_{3} & 6 & 1 & 6.0000 \\\\\n", "{\\color{red}{t}}_{4} & 20 & 5 & 4.0000\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B rhs| Ent Coc]\n", "[ t1 6| 1 6.0000]\n", "[ t2 8| 3 2.6667]\n", "[ t3 6| 1 6.0000]\n", "[ t4 20| 5 4.0000]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cocientes(4)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " \n", " Matriz Inversa\n" ] }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrr|r}\n", "{Basic} & {\\color{red}{t}}_{1} & {x}_{4} & {\\color{red}{t}}_{3} & {\\color{red}{t}}_{4} & {b} \\\\\n", "\\hline\n", " {\\color{red}{t}}_{1} & 1 & -\\frac{1}{3} & 0 & 0 & \\frac{10}{3} \\\\\n", "{x}_{4} & 0 & \\frac{1}{3} & 0 & 0 & \\frac{8}{3} \\\\\n", "{\\color{red}{t}}_{3} & 0 & -\\frac{1}{3} & 1 & 0 & \\frac{10}{3} \\\\\n", "{\\color{red}{t}}_{4} & 0 & -\\frac{5}{3} & 0 & 1 & \\frac{20}{3} \\\\\n", "\\hline\n", " {\\pi_B} & 1 & -\\frac{7}{3} & 1 & 1 & \\frac{40}{3}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| t1 x4 t3 t4| rhs]\n", "[----+-------------------+----]\n", "[ t1| 1 -1/3 0 0|10/3]\n", "[ x4| 0 1/3 0 0| 8/3]\n", "[ t3| 0 -1/3 1 0|10/3]\n", "[ t4| 0 -5/3 0 1|20/3]\n", "[----+-------------------+----]\n", "[ WPI| 1 -7/3 1 1|40/3]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Fila Indicadora\n" ] }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrrrrrrrrr}\n", "{x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {\\color{red}{t}}_{3} & {\\color{red}{t}}_{4} \\\\\n", "\\hline\n", " -\\frac{8}{3} & -\\frac{14}{3} & -4 & 0 & -\\frac{4}{3} & -\\frac{2}{3} & 0 & \\frac{10}{3} & 0 & 0\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ x1 x2 x3 x4 x5 x6 t1 t2 t3 t4]\n", "[-----------------------------------------------------------]\n", "[ -8/3 -14/3 -4 0 -4/3 -2/3 0 10/3 0 0]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ " \n" ] } ], "source": [ "cambio(2,4)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rr|rr}\n", "{Basic} & {b} & {Col\\ Entr} & {Cocientes} \\\\\n", "{\\color{red}{t}}_{1} & \\frac{10}{3} & \\frac{2}{3} & 5.0000 \\\\\n", "{x}_{4} & \\frac{8}{3} & \\frac{1}{3} & 8.0000 \\\\\n", "{\\color{red}{t}}_{3} & \\frac{10}{3} & \\frac{5}{3} & 2.0000 \\\\\n", "{\\color{red}{t}}_{4} & \\frac{20}{3} & \\frac{7}{3} & 2.8571\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B rhs| Ent Coc]\n", "[ t1 10/3| 2/3 5.0000]\n", "[ x4 8/3| 1/3 8.0000]\n", "[ t3 10/3| 5/3 2.0000]\n", "[ t4 20/3| 7/3 2.8571]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cocientes(2)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " \n", " Matriz Inversa\n" ] }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrr|r}\n", "{Basic} & {\\color{red}{t}}_{1} & {x}_{4} & {x}_{2} & {\\color{red}{t}}_{4} & {b} \\\\\n", "\\hline\n", " {\\color{red}{t}}_{1} & 1 & -\\frac{1}{5} & -\\frac{2}{5} & 0 & 2 \\\\\n", "{x}_{4} & 0 & \\frac{2}{5} & -\\frac{1}{5} & 0 & 2 \\\\\n", "{x}_{2} & 0 & -\\frac{1}{5} & \\frac{3}{5} & 0 & 2 \\\\\n", "{\\color{red}{t}}_{4} & 0 & -\\frac{6}{5} & -\\frac{7}{5} & 1 & 2 \\\\\n", "\\hline\n", " {\\pi_B} & 1 & -\\frac{7}{5} & -\\frac{9}{5} & 1 & 4\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| t1 x4 x2 t4| rhs]\n", "[----+-------------------+----]\n", "[ t1| 1 -1/5 -2/5 0| 2]\n", "[ x4| 0 2/5 -1/5 0| 2]\n", "[ x2| 0 -1/5 3/5 0| 2]\n", "[ t4| 0 -6/5 -7/5 1| 2]\n", "[----+-------------------+----]\n", "[ WPI| 1 -7/5 -9/5 1| 4]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Fila Indicadora\n" ] }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrrrrrrrrr}\n", "{x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {\\color{red}{t}}_{3} & {\\color{red}{t}}_{4} \\\\\n", "\\hline\n", " -\\frac{4}{5} & 0 & -\\frac{6}{5} & 0 & -\\frac{2}{5} & -\\frac{8}{5} & 0 & \\frac{12}{5} & \\frac{14}{5} & 0\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ x1 x2 x3 x4 x5 x6 t1 t2 t3 t4]\n", "[-------------------------------------------------]\n", "[-4/5 0 -6/5 0 -2/5 -8/5 0 12/5 14/5 0]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ " \n" ] } ], "source": [ "cambio(3,2)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rr|rr}\n", "{Basic} & {b} & {Col\\ Entr} & {Cocientes} \\\\\n", "{\\color{red}{t}}_{1} & 2 & \\frac{4}{5} & 2.5000 \\\\\n", "{x}_{4} & 2 & \\frac{2}{5} & 5.0000 \\\\\n", "{x}_{2} & 2 & -\\frac{1}{5} & \\mathit{NO} \\\\\n", "{\\color{red}{t}}_{4} & 2 & \\frac{4}{5} & 2.5000\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B rhs| Ent Coc]\n", "[ t1 2| 4/5 2.5000]\n", "[ x4 2| 2/5 5.0000]\n", "[ x2 2| -1/5 NO]\n", "[ t4 2| 4/5 2.5000]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cocientes(6)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " \n", " Matriz Inversa\n" ] }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrr|r}\n", "{Basic} & {x}_{6} & {x}_{4} & {x}_{2} & {\\color{red}{t}}_{4} & {b} \\\\\n", "\\hline\n", " {x}_{6} & \\frac{5}{4} & -\\frac{1}{4} & -\\frac{1}{2} & 0 & \\frac{5}{2} \\\\\n", "{x}_{4} & -\\frac{1}{2} & \\frac{1}{2} & 0 & 0 & 1 \\\\\n", "{x}_{2} & \\frac{1}{4} & -\\frac{1}{4} & \\frac{1}{2} & 0 & \\frac{5}{2} \\\\\n", "{\\color{red}{t}}_{4} & -1 & -1 & -1 & 1 & 0 \\\\\n", "\\hline\n", " {\\pi_B} & -1 & -1 & -1 & 1 & 0\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x6 x4 x2 t4| rhs]\n", "[----+-------------------+----]\n", "[ x6| 5/4 -1/4 -1/2 0| 5/2]\n", "[ x4|-1/2 1/2 0 0| 1]\n", "[ x2| 1/4 -1/4 1/2 0| 5/2]\n", "[ t4| -1 -1 -1 1| 0]\n", "[----+-------------------+----]\n", "[ WPI| -1 -1 -1 1| 0]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Fila Indicadora\n" ] }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrrrrrrrrr}\n", "{x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {\\color{red}{t}}_{3} & {\\color{red}{t}}_{4} \\\\\n", "\\hline\n", " 0 & 0 & 0 & 0 & 0 & 0 & 2 & 2 & 2 & 0\n", "\\end{array}\\right)$$" ], "text/plain": [ "[x1 x2 x3 x4 x5 x6 t1 t2 t3 t4]\n", "[-----------------------------]\n", "[ 0 0 0 0 0 0 2 2 2 0]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ " \n" ] } ], "source": [ "cambio(1,6)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{red}{t}}_{1} & {\\color{red}{t}}_{2} & {\\color{red}{t}}_{3} & {\\color{red}{t}}_{4} & {b} \\\\\n", "\\hline\n", " {x}_{6} & \\frac{1}{2} & 0 & \\frac{3}{4} & 0 & \\frac{1}{4} & 1 & \\frac{5}{4} & -\\frac{1}{4} & -\\frac{1}{2} & 0 & \\frac{5}{2} \\\\\n", "{x}_{4} & 0 & 0 & -\\frac{1}{2} & 1 & \\frac{1}{2} & 0 & -\\frac{1}{2} & \\frac{1}{2} & 0 & 0 & 1 \\\\\n", "{x}_{2} & \\frac{1}{2} & 1 & \\frac{3}{4} & 0 & \\frac{1}{4} & 0 & \\frac{1}{4} & -\\frac{1}{4} & \\frac{1}{2} & 0 & \\frac{5}{2} \\\\\n", "{\\color{red}{t}}_{4} & 0 & 0 & 0 & 0 & 0 & 0 & -1 & -1 & -1 & 1 & 0 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 0 & 2 & 2 & 2 & 0 & 0\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 x5 x6 t1 t2 t3 t4| rhs]\n", "[----+-------------------------------------------------+----]\n", "[ x6| 1/2 0 3/4 0 1/4 1 5/4 -1/4 -1/2 0| 5/2]\n", "[ x4| 0 0 -1/2 1 1/2 0 -1/2 1/2 0 0| 1]\n", "[ x2| 1/2 1 3/4 0 1/4 0 1/4 -1/4 1/2 0| 5/2]\n", "[ t4| 0 0 0 0 0 0 -1 -1 -1 1| 0]\n", "[----+-------------------------------------------------+----]\n", "[ W| 0 0 0 0 0 0 2 2 2 0| 0]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cuadroI()" ] }, { "cell_type": "code", "execution_count": 24, "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": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\ \\ \\ Fase\\ II}$$" ], "text/plain": [ "FII" ] }, "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": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {b} \\\\\n", "\\hline\n", " {x}_{6} & \\frac{1}{2} & 0 & \\frac{3}{4} & 0 & \\frac{1}{4} & 1 & \\frac{5}{2} \\\\\n", "{x}_{4} & 0 & 0 & -\\frac{1}{2} & 1 & \\frac{1}{2} & 0 & 1 \\\\\n", "{x}_{2} & \\frac{1}{2} & 1 & \\frac{3}{4} & 0 & \\frac{1}{4} & 0 & \\frac{5}{2} \\\\\n", "\\hline\n", " {W_{ind}} & -5 & 0 & -\\frac{3}{2} & 0 & \\frac{7}{2} & 0 & 93\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 x5 x6| rhs]\n", "[----+-----------------------------+----]\n", "[ x6| 1/2 0 3/4 0 1/4 1| 5/2]\n", "[ x4| 0 0 -1/2 1 1/2 0| 1]\n", "[ x2| 1/2 1 3/4 0 1/4 0| 5/2]\n", "[----+-----------------------------+----]\n", "[ W| -5 0 -3/2 0 7/2 0| 93]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "nnart=1; tt=[0,0,0,1]; faseII(nnart,tt)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rr|rr}\n", "{Basic} & {b} & {Col\\ Entr} & {Cocientes} \\\\\n", "{x}_{6} & \\frac{5}{2} & \\frac{1}{4} & 10.000 \\\\\n", "{x}_{4} & 1 & \\frac{1}{2} & 2.0000 \\\\\n", "{x}_{2} & \\frac{5}{2} & \\frac{1}{4} & 10.000\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B rhs| Ent Coc]\n", "[ x6 5/2| 1/4 10.000]\n", "[ x4 1| 1/2 2.0000]\n", "[ x2 5/2| 1/4 10.000]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cocientes(5)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " \n", " Matriz Inversa\n" ] }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrr|r}\n", "{Basic} & {x}_{6} & {x}_{5} & {x}_{2} & {b} \\\\\n", "\\hline\n", " {x}_{6} & \\frac{3}{2} & -\\frac{1}{2} & -\\frac{1}{2} & 2 \\\\\n", "{x}_{5} & -1 & 1 & 0 & 2 \\\\\n", "{x}_{2} & \\frac{1}{2} & -\\frac{1}{2} & \\frac{1}{2} & 2 \\\\\n", "\\hline\n", " {\\pi_B} & 11 & 5 & -1 & 100\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x6 x5 x2| rhs]\n", "[----+--------------+----]\n", "[ x6| 3/2 -1/2 -1/2| 2]\n", "[ x5| -1 1 0| 2]\n", "[ x2| 1/2 -1/2 1/2| 2]\n", "[----+--------------+----]\n", "[ ZPI| 11 5 -1| 100]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Fila Indicadora\n" ] }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrrrrr}\n", "{x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} \\\\\n", "\\hline\n", " -5 & 0 & 2 & -7 & 0 & 0\n", "\\end{array}\\right)$$" ], "text/plain": [ "[x1 x2 x3 x4 x5 x6]\n", "[-----------------]\n", "[-5 0 2 -7 0 0]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ " \n" ] } ], "source": [ "cambio(2,5)" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rr|rr}\n", "{Basic} & {b} & {Col\\ Entr} & {Cocientes} \\\\\n", "{x}_{6} & 2 & 1 & 2.0000 \\\\\n", "{x}_{5} & 2 & -1 & \\mathit{NO} \\\\\n", "{x}_{2} & 2 & 1 & 2.0000\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B rhs| Ent Coc]\n", "[ x6 2| 1 2.0000]\n", "[ x5 2| -1 NO]\n", "[ x2 2| 1 2.0000]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cocientes(3)" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " \n", " Matriz Inversa\n" ] }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrr|r}\n", "{Basic} & {x}_{3} & {x}_{5} & {x}_{2} & {b} \\\\\n", "\\hline\n", " {x}_{3} & \\frac{3}{2} & -\\frac{1}{2} & -\\frac{1}{2} & 2 \\\\\n", "{x}_{5} & \\frac{1}{2} & \\frac{1}{2} & -\\frac{1}{2} & 4 \\\\\n", "{x}_{2} & -1 & 0 & 1 & 0 \\\\\n", "\\hline\n", " {\\pi_B} & 14 & 4 & -2 & 104\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x3 x5 x2| rhs]\n", "[----+--------------+----]\n", "[ x3| 3/2 -1/2 -1/2| 2]\n", "[ x5| 1/2 1/2 -1/2| 4]\n", "[ x2| -1 0 1| 0]\n", "[----+--------------+----]\n", "[ ZPI| 14 4 -2| 104]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Fila Indicadora\n" ] }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrrrrr}\n", "{x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} \\\\\n", "\\hline\n", " -6 & 0 & 0 & -6 & 0 & -2\n", "\\end{array}\\right)$$" ], "text/plain": [ "[x1 x2 x3 x4 x5 x6]\n", "[-----------------]\n", "[-6 0 0 -6 0 -2]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ " \n" ] } ], "source": [ "cambio(1,3)" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {b} \\\\\n", "\\hline\n", " {x}_{3} & \\frac{1}{2} & 0 & 1 & -\\frac{1}{2} & 0 & 1 & 2 \\\\\n", "{x}_{5} & \\frac{1}{2} & 0 & 0 & \\frac{3}{2} & 1 & 1 & 4 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & -1 & 0 \\\\\n", "\\hline\n", " {W_{ind}} & -6 & 0 & 0 & -6 & 0 & -2 & 104\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 x5 x6| rhs]\n", "[----+-----------------------------+----]\n", "[ x3| 1/2 0 1 -1/2 0 1| 2]\n", "[ x5| 1/2 0 0 3/2 1 1| 4]\n", "[ x2| 0 1 0 0 0 -1| 0]\n", "[----+-----------------------------+----]\n", "[ W| -6 0 0 -6 0 -2| 104]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cuadroII()" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{green}{s}}_{4} & {b} \\\\\n", "\\hline\n", " {x}_{3} & \\frac{1}{2} & 0 & 1 & -\\frac{1}{2} & 0 & 1 & 0 & 2 \\\\\n", "{x}_{5} & \\frac{1}{2} & 0 & 0 & \\frac{3}{2} & 1 & 1 & 0 & 4 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & -1 & 0 & 0 \\\\\n", "{\\color{green}{s}}_{4} & -3 & 0 & 0 & -2 & 0 & 0 & 1 & -5 \\\\\n", "\\hline\n", " {Z_{ind}} & -6 & 0 & 0 & -6 & 0 & -2 & 0 & 104\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 x5 x6 s4| rhs]\n", "[----+----------------------------------+----]\n", "[ x3| 1/2 0 1 -1/2 0 1 0| 2]\n", "[ x5| 1/2 0 0 3/2 1 1 0| 4]\n", "[ x2| 0 1 0 0 0 -1 0| 0]\n", "[ s4| -3 0 0 -2 0 0 1| -5]\n", "[----+----------------------------------+----]\n", "[ Z| -6 0 0 -6 0 -2 0| 104]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "v=matrix(QQ,1,n,[1,2,3,4,5,6]); R=21; añade(v,R)" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{green}{s}}_{4} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{4} & -3 & 0 & 0 & -2 & 0 & 0 & 1 \\\\\n", "\\hline\n", " {Z_{ind}} & -6 & 0 & 0 & -6 & 0 & -2 & 0 \\\\\n", "\\hline\n", " {Cocientes} & 2.0000 & \\mathit{NO} & \\mathit{NO} & 3.0000 & \\mathit{NO} & \\mathit{NO} & \\mathit{NO}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 x5 x6 s4]\n", "[------+------------------------------------------------]\n", "[ s4| -3 0 0 -2 0 0 1]\n", "[------+------------------------------------------------]\n", "[ Z| -6 0 0 -6 0 -2 0]\n", "[------+------------------------------------------------]\n", "[ Coc|2.0000 NO NO 3.0000 NO NO NO]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cocientesD(4)" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " \n", " Matriz Inversa\n" ] }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrr|r}\n", "{Basic} & {x}_{3} & {x}_{5} & {x}_{2} & {x}_{1} & {b} \\\\\n", "\\hline\n", " {x}_{3} & \\frac{2}{3} & -\\frac{2}{3} & -\\frac{1}{6} & \\frac{1}{6} & \\frac{7}{6} \\\\\n", "{x}_{5} & -\\frac{1}{3} & \\frac{1}{3} & -\\frac{1}{6} & \\frac{1}{6} & \\frac{19}{6} \\\\\n", "{x}_{2} & -1 & 0 & 1 & 0 & 0 \\\\\n", "{x}_{1} & \\frac{5}{3} & \\frac{1}{3} & -\\frac{2}{3} & -\\frac{1}{3} & \\frac{5}{3} \\\\\n", "\\hline\n", " {\\pi_B} & 4 & 2 & 2 & 2 & 94\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x3 x5 x2 x1| rhs]\n", "[----+-------------------+----]\n", "[ x3| 2/3 -2/3 -1/6 1/6| 7/6]\n", "[ x5|-1/3 1/3 -1/6 1/6|19/6]\n", "[ x2| -1 0 1 0| 0]\n", "[ x1| 5/3 1/3 -2/3 -1/3| 5/3]\n", "[----+-------------------+----]\n", "[ ZPI| 4 2 2 2| 94]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Fila Indicadora\n" ] }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrrrrrr}\n", "{x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{green}{s}}_{4} \\\\\n", "\\hline\n", " 0 & 0 & 0 & -2 & 0 & -2 & -2\n", "\\end{array}\\right)$$" ], "text/plain": [ "[x1 x2 x3 x4 x5 x6 s4]\n", "[--------------------]\n", "[ 0 0 0 -2 0 -2 -2]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ " \n" ] } ], "source": [ "cambio(4,1)" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{green}{s}}_{4} & {b} \\\\\n", "\\hline\n", " {x}_{3} & 0 & 0 & 1 & -\\frac{5}{6} & 0 & 1 & \\frac{1}{6} & \\frac{7}{6} \\\\\n", "{x}_{5} & 0 & 0 & 0 & \\frac{7}{6} & 1 & 1 & \\frac{1}{6} & \\frac{19}{6} \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & -1 & 0 & 0 \\\\\n", "{x}_{1} & 1 & 0 & 0 & \\frac{2}{3} & 0 & 0 & -\\frac{1}{3} & \\frac{5}{3} \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & -2 & 0 & -2 & -2 & 94\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 x5 x6 s4| rhs]\n", "[----+----------------------------------+----]\n", "[ x3| 0 0 1 -5/6 0 1 1/6| 7/6]\n", "[ x5| 0 0 0 7/6 1 1 1/6|19/6]\n", "[ x2| 0 1 0 0 0 -1 0| 0]\n", "[ x1| 1 0 0 2/3 0 0 -1/3| 5/3]\n", "[----+----------------------------------+----]\n", "[ W| 0 0 0 -2 0 -2 -2| 94]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cuadroII()" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [], "source": [ "#b1p=matrix(QQ,m,1,[0,1,0,0]); b2p=matrix(QQ,m,1,[1,0,0,0]);param2b(b1p,b2p)" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {x}_{6} & {\\color{green}{s}}_{4} & {b} \\\\\n", "\\hline\n", " {x}_{3} & 0 & 0 & 1 & -\\frac{5}{6} & 0 & 1 & \\frac{1}{6} & \\frac{7}{6} \\\\\n", "{x}_{5} & 0 & 0 & 0 & \\frac{7}{6} & 1 & 1 & \\frac{1}{6} & \\frac{19}{6} \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & 0 & -1 & 0 & 0 \\\\\n", "{x}_{1} & 1 & 0 & 0 & \\frac{2}{3} & 0 & 0 & -\\frac{1}{3} & \\frac{5}{3} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & -2 & 0 & -2 & -2 & 94 \\\\\n", "{Z{1p}} & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\\\\n", "{Z{2p}} & 0 & 0 & 0 & -\\frac{2}{3} & 0 & 0 & \\frac{1}{3} & \\frac{5}{3}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 x5 x6 s4| rhs]\n", "[----+----------------------------------+----]\n", "[ x3| 0 0 1 -5/6 0 1 1/6| 7/6]\n", "[ x5| 0 0 0 7/6 1 1 1/6|19/6]\n", "[ x2| 0 1 0 0 0 -1 0| 0]\n", "[ x1| 1 0 0 2/3 0 0 -1/3| 5/3]\n", "[----+----------------------------------+----]\n", "[ Z| 0 0 0 -2 0 -2 -2| 94]\n", "[ Z1p| 0 0 0 0 0 1 0| 0]\n", "[ Z2p| 0 0 0 -2/3 0 0 1/3| 5/3]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "c1p=matrix(QQ,1,nvar,[0,1,0,0,0,0,0]); c2p=matrix(QQ,1,nvar,[1,0,0,0,0,0,0]);param2c(c1p,c2p)" ] } ], "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 }