{ "cells": [ { "cell_type": "code", "execution_count": 112, "metadata": { "scrolled": false }, "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": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n", "\\begin{array}{lcrcrcrcrcl}\n", " \\max \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 7 x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 12 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 17 x_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 12 x_{4} \\mspace{-6mu}&\\mspace{-6mu} 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y_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 16 y_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 14 y_{3} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 6 y_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 4 y_{3} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 7 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 6 y_{1} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 7 y_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 4 y_{3} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 12 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 7 y_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 5 y_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 y_{3} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 17 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 7 y_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} y_{2} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 2 y_{3} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 12 \\\\\n", "\\end{array} \\\\\n", "y_{1}, y_{2}, y_{3} \\geq 0\n", "\\end{array}$$" ], "text/plain": [ "LP problem (use 'view(...)' or '%display typeset' for details)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{2197}{10}$$" ], "text/plain": [ "2197/10" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\frac{361}{120},\\,\\frac{29}{6},\\,\\frac{1667}{240}\\right)$$" ], "text/plain": [ "(361/120, 29/6, 1667/240)" ] }, "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": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 1 & 6 & -7 & 7 & 1 & 0 & 0 & 15 \\\\\n", "{\\color{green}{s}}_{2} & 6 & -7 & 5 & 1 & 0 & 1 & 0 & 16 \\\\\n", "{\\color{green}{s}}_{3} & 4 & 4 & 2 & -2 & 0 & 0 & 1 & 14 \\\\\n", "\\hline\n", " {Z_{ind}} & 7 & 12 & 17 & 12 & 0 & 0 & 0 & 0\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3|rhs]\n", "[---+---------------------------+---]\n", "[ s1| 1 6 -7 7 1 0 0| 15]\n", "[ s2| 6 -7 5 1 0 1 0| 16]\n", "[ s3| 4 4 2 -2 0 0 1| 14]\n", "[---+---------------------------+---]\n", "[ Z| 7 12 17 12 0 0 0| 0]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ " \n", "(Es un problema de tipo maximizar)\n", " \n", "cambio( 2 , 3 )\n", "cambio( 3 , 2 )\n", "cambio( 1 , 4 )\n" ] }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {b} \\\\\n", "\\hline\n", " {x}_{4} & \\frac{35}{24} & 0 & 0 & 1 & \\frac{17}{120} & \\frac{1}{6} & \\frac{19}{240} & \\frac{59}{10} \\\\\n", "{x}_{3} & \\frac{47}{24} & 0 & 1 & 0 & \\frac{1}{24} & \\frac{1}{6} & \\frac{11}{48} & \\frac{13}{2} \\\\\n", "{x}_{2} & \\frac{3}{4} & 1 & 0 & 0 & \\frac{1}{20} & 0 & \\frac{7}{40} & \\frac{16}{5} \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{1267}{24} & 0 & 0 & 0 & -\\frac{361}{120} & -\\frac{29}{6} & -\\frac{1667}{240} & \\frac{2197}{10}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3| rhs]\n", "[---------+---------------------------------------------------------------------+---------]\n", "[ x4| 35/24 0 0 1 17/120 1/6 19/240| 59/10]\n", "[ x3| 47/24 0 1 0 1/24 1/6 11/48| 13/2]\n", "[ x2| 3/4 1 0 0 1/20 0 7/40| 16/5]\n", "[---------+---------------------------------------------------------------------+---------]\n", "[ Z| -1267/24 0 0 0 -361/120 -29/6 -1667/240| 2197/10]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "El problema es óptimo\n" ] } ], "source": [ "tipo='max' #max o min\n", "n=4 # número de variables x's\n", "m=3 # número de restricciones (distintas de las de signo)\n", "\n", "\n", "c=matrix(QQ,1,n,[7,12,17,12] ) # vector de costos\n", "\n", "A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n", "[1,6,-7,7],\n", "[6,-7,5,1],\n", "[4,4,2,-2]\n", "])\n", "\n", "b=matrix(QQ,m,1,[15,16,14]) # vector de la derecha\n", "\n", "\n", "\n", "######################################################\n", "############### VARIABLES DE HOLGURA ################\n", "\n", "\n", "h=matrix(ZZ,1,m,[1,1,1]) # variables de holgura: \n", " # Pon 1 si va sumando, \n", " # -1 si va restando y \n", " # 0 si no hay variable de holgura.\n", "\n", "#######################################################\n", "\n", "####################################################################\n", "############ HASTA AQUÍ LOS DATOS ################################\n", "####################################################################\n", "\n", "load('https://sage.unex.es/501708/SAGE/simplex2023Auto_MC.sage')\n", "#load('https://sage.unex.es/501708/SAGE/simplex2023AutoREVISED.sage')\n", "#load('https://sage.unex.es/501708/SAGE/simplex2023Auto.sage')\n", "\n" ] }, { "cell_type": "code", "execution_count": 94, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[1, 2, 3, 4, 5, 6, 7\\right]$$" ], "text/plain": [ "[1, 2, 3, 4, 5, 6, 7]" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "[9/10, 1/2, 1/5]" ] }, "execution_count": 94, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pardec()" ] }, { "cell_type": "code", "execution_count": 95, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[1, 2, 3, 4, 5, 6, 7\\right]$$" ], "text/plain": [ "[1, 2, 3, 4, 5, 6, 7]" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} \\\\\n", "\\hline\n", " {x}_{4} & \\frac{35}{24} & 0 & 0 & 1 & \\frac{17}{120} & \\frac{1}{6} & \\frac{19}{240} & 0 & \\frac{59}{10} \\\\\n", "{x}_{3} & \\frac{47}{24} & 0 & 1 & 0 & \\frac{1}{24} & \\frac{1}{6} & \\frac{11}{48} & 0 & \\frac{13}{2} \\\\\n", "{x}_{2} & \\frac{3}{4} & 1 & 0 & 0 & \\frac{1}{20} & 0 & \\frac{7}{40} & 0 & \\frac{16}{5} \\\\\n", "{\\color{green}{s}}_{4} & -\\frac{1}{24} & 0 & 0 & 0 & -\\frac{1}{24} & -\\frac{1}{6} & -\\frac{11}{48} & 1 & -\\frac{1}{2} \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{1267}{24} & 0 & 0 & 0 & -\\frac{361}{120} & -\\frac{29}{6} & -\\frac{1667}{240} & 0 & \\frac{2197}{10}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4| rhs]\n", "[---------+-------------------------------------------------------------------------------+---------]\n", "[ x4| 35/24 0 0 1 17/120 1/6 19/240 0| 59/10]\n", "[ x3| 47/24 0 1 0 1/24 1/6 11/48 0| 13/2]\n", "[ x2| 3/4 1 0 0 1/20 0 7/40 0| 16/5]\n", "[ s4| -1/24 0 0 0 -1/24 -1/6 -11/48 1| -1/2]\n", "[---------+-------------------------------------------------------------------------------+---------]\n", "[ Z| -1267/24 0 0 0 -361/120 -29/6 -1667/240 0| 2197/10]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "corte(2) # 1" ] }, { "cell_type": "code", "execution_count": 96, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[1267.0 NO NO NO 72.200 29.000 30.309 NO]" ] }, "execution_count": 96, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cocientesD(4)" ] }, { "cell_type": "code", "execution_count": 97, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} \\\\\n", "\\hline\n", " {x}_{4} & \\frac{17}{12} & 0 & 0 & 1 & \\frac{1}{10} & 0 & -\\frac{3}{20} & 1 & \\frac{27}{5} \\\\\n", "{x}_{3} & \\frac{23}{12} & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 6 \\\\\n", "{x}_{2} & \\frac{3}{4} & 1 & 0 & 0 & \\frac{1}{20} & 0 & \\frac{7}{40} & 0 & \\frac{16}{5} \\\\\n", "{\\color{green}{s}}_{2} & \\frac{1}{4} & 0 & 0 & 0 & \\frac{1}{4} & 1 & \\frac{11}{8} & -6 & 3 \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{619}{12} & 0 & 0 & 0 & -\\frac{9}{5} & 0 & -\\frac{3}{10} & -29 & \\frac{1026}{5}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4| rhs]\n", "[-------+---------------------------------------------------------------+-------]\n", "[ x4| 17/12 0 0 1 1/10 0 -3/20 1| 27/5]\n", "[ x3| 23/12 0 1 0 0 0 0 1| 6]\n", "[ x2| 3/4 1 0 0 1/20 0 7/40 0| 16/5]\n", "[ s2| 1/4 0 0 0 1/4 1 11/8 -6| 3]\n", "[-------+---------------------------------------------------------------+-------]\n", "[ Z|-619/12 0 0 0 -9/5 0 -3/10 -29| 1026/5]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(4,6)" ] }, { "cell_type": "code", "execution_count": 98, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[1, 2, 3, 4, 5, 6, 7\\right]$$" ], "text/plain": [ "[1, 2, 3, 4, 5, 6, 7]" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "[2/5, 0, 1/5, 0]" ] }, "execution_count": 98, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pardec()" ] }, { "cell_type": "code", "execution_count": 99, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[1, 2, 3, 4, 5, 6, 7\\right]$$" ], "text/plain": [ "[1, 2, 3, 4, 5, 6, 7]" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {b} \\\\\n", "\\hline\n", " {x}_{4} & \\frac{17}{12} & 0 & 0 & 1 & \\frac{1}{10} & 0 & -\\frac{3}{20} & 1 & 0 & \\frac{27}{5} \\\\\n", "{x}_{3} & \\frac{23}{12} & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 6 \\\\\n", "{x}_{2} & \\frac{3}{4} & 1 & 0 & 0 & \\frac{1}{20} & 0 & \\frac{7}{40} & 0 & 0 & \\frac{16}{5} \\\\\n", "{\\color{green}{s}}_{2} & \\frac{1}{4} & 0 & 0 & 0 & \\frac{1}{4} & 1 & \\frac{11}{8} & -6 & 0 & 3 \\\\\n", "{\\color{green}{s}}_{5} & -\\frac{1}{16} & 0 & 0 & 0 & -\\frac{1}{20} & 0 & -\\frac{7}{40} & 0 & 1 & -\\frac{1}{5} \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{619}{12} & 0 & 0 & 0 & -\\frac{9}{5} & 0 & -\\frac{3}{10} & -29 & 0 & \\frac{1026}{5}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5| rhs]\n", "[-------+-----------------------------------------------------------------------+-------]\n", "[ x4| 17/12 0 0 1 1/10 0 -3/20 1 0| 27/5]\n", "[ x3| 23/12 0 1 0 0 0 0 1 0| 6]\n", "[ x2| 3/4 1 0 0 1/20 0 7/40 0 0| 16/5]\n", "[ s2| 1/4 0 0 0 1/4 1 11/8 -6 0| 3]\n", "[ s5| -1/16 0 0 0 -1/20 0 -7/40 0 1| -1/5]\n", "[-------+-----------------------------------------------------------------------+-------]\n", "[ Z|-619/12 0 0 0 -9/5 0 -3/10 -29 0| 1026/5]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "corte(3)" ] }, { "cell_type": "code", "execution_count": 100, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[825.33 NO NO NO 36.000 NO 1.7143 NO NO]" ] }, "execution_count": 100, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cocientesD(5)" ] }, { "cell_type": "code", "execution_count": 101, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {b} \\\\\n", "\\hline\n", " {x}_{4} & \\frac{247}{168} & 0 & 0 & 1 & \\frac{1}{7} & 0 & 0 & 1 & -\\frac{6}{7} & \\frac{39}{7} \\\\\n", "{x}_{3} & \\frac{23}{12} & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 6 \\\\\n", "{x}_{2} & \\frac{11}{16} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 3 \\\\\n", "{\\color{green}{s}}_{2} & -\\frac{27}{112} & 0 & 0 & 0 & -\\frac{1}{7} & 1 & 0 & -6 & \\frac{55}{7} & \\frac{10}{7} \\\\\n", "{\\color{green}{s}}_{3} & \\frac{5}{14} & 0 & 0 & 0 & \\frac{2}{7} & 0 & 1 & 0 & -\\frac{40}{7} & \\frac{8}{7} \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{1081}{21} & 0 & 0 & 0 & -\\frac{12}{7} & 0 & 0 & -29 & -\\frac{12}{7} & \\frac{1434}{7}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5| rhs]\n", "[--------+--------------------------------------------------------------------------------+--------]\n", "[ x4| 247/168 0 0 1 1/7 0 0 1 -6/7| 39/7]\n", "[ x3| 23/12 0 1 0 0 0 0 1 0| 6]\n", "[ x2| 11/16 1 0 0 0 0 0 0 1| 3]\n", "[ s2| -27/112 0 0 0 -1/7 1 0 -6 55/7| 10/7]\n", "[ s3| 5/14 0 0 0 2/7 0 1 0 -40/7| 8/7]\n", "[--------+--------------------------------------------------------------------------------+--------]\n", "[ Z|-1081/21 0 0 0 -12/7 0 0 -29 -12/7| 1434/7]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(5,7)" ] }, { "cell_type": "code", "execution_count": 102, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[1, 2, 3, 4, 5, 6, 7\\right]$$" ], "text/plain": [ "[1, 2, 3, 4, 5, 6, 7]" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "[4/7, 0, 0, 3/7, 1/7]" ] }, "execution_count": 102, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pardec()" ] }, { "cell_type": "code", "execution_count": 103, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[1, 2, 3, 4, 5, 6, 7\\right]$$" ], "text/plain": [ "[1, 2, 3, 4, 5, 6, 7]" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {x}_{4} & \\frac{247}{168} & 0 & 0 & 1 & \\frac{1}{7} & 0 & 0 & 1 & -\\frac{6}{7} & 0 & \\frac{39}{7} \\\\\n", "{x}_{3} & \\frac{23}{12} & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 6 \\\\\n", "{x}_{2} & \\frac{11}{16} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 3 \\\\\n", "{\\color{green}{s}}_{2} & -\\frac{27}{112} & 0 & 0 & 0 & -\\frac{1}{7} & 1 & 0 & -6 & \\frac{55}{7} & 0 & \\frac{10}{7} \\\\\n", "{\\color{green}{s}}_{3} & \\frac{5}{14} & 0 & 0 & 0 & \\frac{2}{7} & 0 & 1 & 0 & -\\frac{40}{7} & 0 & \\frac{8}{7} \\\\\n", "{\\color{green}{s}}_{6} & -\\frac{79}{168} & 0 & 0 & 0 & -\\frac{1}{7} & 0 & 0 & -1 & -\\frac{8}{7} & 1 & -\\frac{4}{7} \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{1081}{21} & 0 & 0 & 0 & -\\frac{12}{7} & 0 & 0 & -29 & -\\frac{12}{7} & 0 & \\frac{1434}{7}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n", "[--------+-----------------------------------------------------------------------------------------+--------]\n", "[ x4| 247/168 0 0 1 1/7 0 0 1 -6/7 0| 39/7]\n", "[ x3| 23/12 0 1 0 0 0 0 1 0 0| 6]\n", "[ x2| 11/16 1 0 0 0 0 0 0 1 0| 3]\n", "[ s2| -27/112 0 0 0 -1/7 1 0 -6 55/7 0| 10/7]\n", "[ s3| 5/14 0 0 0 2/7 0 1 0 -40/7 0| 8/7]\n", "[ s6| -79/168 0 0 0 -1/7 0 0 -1 -8/7 1| -4/7]\n", "[--------+-----------------------------------------------------------------------------------------+--------]\n", "[ Z|-1081/21 0 0 0 -12/7 0 0 -29 -12/7 0| 1434/7]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "corte(1)" ] }, { "cell_type": "code", "execution_count": 104, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[109.47 NO NO NO 12.000 NO NO 29.000 1.5000 NO]" ] }, "execution_count": 104, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cocientesD(6)" ] }, { "cell_type": "code", "execution_count": 105, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {x}_{4} & \\frac{175}{96} & 0 & 0 & 1 & \\frac{1}{4} & 0 & 0 & \\frac{7}{4} & 0 & -\\frac{3}{4} & 6 \\\\\n", "{x}_{3} & \\frac{23}{12} & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 6 \\\\\n", "{x}_{2} & \\frac{53}{192} & 1 & 0 & 0 & -\\frac{1}{8} & 0 & 0 & -\\frac{7}{8} & 0 & \\frac{7}{8} & \\frac{5}{2} \\\\\n", "{\\color{green}{s}}_{2} & -\\frac{667}{192} & 0 & 0 & 0 & -\\frac{9}{8} & 1 & 0 & -\\frac{103}{8} & 0 & \\frac{55}{8} & -\\frac{5}{2} \\\\\n", "{\\color{green}{s}}_{3} & \\frac{65}{24} & 0 & 0 & 0 & 1 & 0 & 1 & 5 & 0 & -5 & 4 \\\\\n", "{\\color{green}{s}}_{5} & \\frac{79}{192} & 0 & 0 & 0 & \\frac{1}{8} & 0 & 0 & \\frac{7}{8} & 1 & -\\frac{7}{8} & \\frac{1}{2} \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{2437}{48} & 0 & 0 & 0 & -\\frac{3}{2} & 0 & 0 & -\\frac{55}{2} & 0 & -\\frac{3}{2} & 204\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n", 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"text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {x}_{4} & \\frac{227}{216} & 0 & 0 & 1 & 0 & \\frac{2}{9} & 0 & -\\frac{10}{9} & 0 & \\frac{7}{9} & \\frac{49}{9} \\\\\n", "{x}_{3} & \\frac{23}{12} & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 6 \\\\\n", "{x}_{2} & \\frac{143}{216} & 1 & 0 & 0 & 0 & -\\frac{1}{9} & 0 & \\frac{5}{9} & 0 & \\frac{1}{9} & \\frac{25}{9} \\\\\n", "{\\color{green}{s}}_{1} & \\frac{667}{216} & 0 & 0 & 0 & 1 & -\\frac{8}{9} & 0 & \\frac{103}{9} & 0 & -\\frac{55}{9} & \\frac{20}{9} \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{41}{108} & 0 & 0 & 0 & 0 & \\frac{8}{9} & 1 & -\\frac{58}{9} & 0 & \\frac{10}{9} & \\frac{16}{9} \\\\\n", "{\\color{green}{s}}_{5} & \\frac{11}{432} & 0 & 0 & 0 & 0 & \\frac{1}{9} & 0 & -\\frac{5}{9} & 1 & -\\frac{1}{9} & \\frac{2}{9} \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{1661}{36} & 0 & 0 & 0 & 0 & -\\frac{4}{3} & 0 & -\\frac{31}{3} & 0 & -\\frac{32}{3} & \\frac{602}{3}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n", "[--------+-----------------------------------------------------------------------------------------+--------]\n", "[ x4| 227/216 0 0 1 0 2/9 0 -10/9 0 7/9| 49/9]\n", "[ x3| 23/12 0 1 0 0 0 0 1 0 0| 6]\n", "[ x2| 143/216 1 0 0 0 -1/9 0 5/9 0 1/9| 25/9]\n", "[ s1| 667/216 0 0 0 1 -8/9 0 103/9 0 -55/9| 20/9]\n", "[ s3| -41/108 0 0 0 0 8/9 1 -58/9 0 10/9| 16/9]\n", "[ s5| 11/432 0 0 0 0 1/9 0 -5/9 1 -1/9| 2/9]\n", "[--------+-----------------------------------------------------------------------------------------+--------]\n", "[ Z|-1661/36 0 0 0 0 -4/3 0 -31/3 0 -32/3| 602/3]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(4,5)" ] }, { "cell_type": "code", "execution_count": 108, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[1, 2, 3, 4, 5, 6, 7\\right]$$" ], "text/plain": [ "[1, 2, 3, 4, 5, 6, 7]" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "[4/9, 0, 7/9, 2/9, 7/9, 2/9]" ] }, "execution_count": 108, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pardec()" ] }, { "cell_type": "code", "execution_count": 109, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[1, 2, 3, 4, 5, 6, 7\\right]$$" ], "text/plain": [ "[1, 2, 3, 4, 5, 6, 7]" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {b} \\\\\n", "\\hline\n", " {x}_{4} & \\frac{227}{216} & 0 & 0 & 1 & 0 & \\frac{2}{9} & 0 & -\\frac{10}{9} & 0 & \\frac{7}{9} & 0 & \\frac{49}{9} \\\\\n", "{x}_{3} & \\frac{23}{12} & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 6 \\\\\n", "{x}_{2} & \\frac{143}{216} & 1 & 0 & 0 & 0 & -\\frac{1}{9} & 0 & \\frac{5}{9} & 0 & \\frac{1}{9} & 0 & \\frac{25}{9} \\\\\n", "{\\color{green}{s}}_{1} & \\frac{667}{216} & 0 & 0 & 0 & 1 & -\\frac{8}{9} & 0 & \\frac{103}{9} & 0 & -\\frac{55}{9} & 0 & \\frac{20}{9} \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{41}{108} & 0 & 0 & 0 & 0 & \\frac{8}{9} & 1 & -\\frac{58}{9} & 0 & \\frac{10}{9} & 0 & \\frac{16}{9} \\\\\n", "{\\color{green}{s}}_{5} & \\frac{11}{432} & 0 & 0 & 0 & 0 & \\frac{1}{9} & 0 & -\\frac{5}{9} & 1 & -\\frac{1}{9} & 0 & \\frac{2}{9} \\\\\n", "{\\color{green}{s}}_{7} & -\\frac{11}{216} & 0 & 0 & 0 & 0 & -\\frac{2}{9} & 0 & -\\frac{8}{9} & 0 & -\\frac{7}{9} & 1 & -\\frac{4}{9} \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{1661}{36} & 0 & 0 & 0 & 0 & -\\frac{4}{3} & 0 & -\\frac{31}{3} & 0 & -\\frac{32}{3} & 0 & \\frac{602}{3}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7| rhs]\n", "[--------+--------------------------------------------------------------------------------------------------+--------]\n", "[ x4| 227/216 0 0 1 0 2/9 0 -10/9 0 7/9 0| 49/9]\n", "[ x3| 23/12 0 1 0 0 0 0 1 0 0 0| 6]\n", "[ x2| 143/216 1 0 0 0 -1/9 0 5/9 0 1/9 0| 25/9]\n", "[ s1| 667/216 0 0 0 1 -8/9 0 103/9 0 -55/9 0| 20/9]\n", "[ s3| -41/108 0 0 0 0 8/9 1 -58/9 0 10/9 0| 16/9]\n", "[ s5| 11/432 0 0 0 0 1/9 0 -5/9 1 -1/9 0| 2/9]\n", "[ s7| -11/216 0 0 0 0 -2/9 0 -8/9 0 -7/9 1| -4/9]\n", "[--------+--------------------------------------------------------------------------------------------------+--------]\n", "[ Z|-1661/36 0 0 0 0 -4/3 0 -31/3 0 -32/3 0| 602/3]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "corte(1)" ] }, { "cell_type": "code", "execution_count": 110, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[906.00 NO NO NO NO 6.0000 NO 11.625 NO 13.714 NO]" ] }, "execution_count": 110, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cocientesD(7)" ] }, { "cell_type": "code", "execution_count": 111, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {b} \\\\\n", "\\hline\n", " {x}_{4} & 1 & 0 & 0 & 1 & 0 & 0 & 0 & -2 & 0 & 0 & 1 & 5 \\\\\n", "{x}_{3} & \\frac{23}{12} & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 6 \\\\\n", "{x}_{2} & \\frac{11}{16} & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & \\frac{1}{2} & -\\frac{1}{2} & 3 \\\\\n", "{\\color{green}{s}}_{1} & \\frac{79}{24} & 0 & 0 & 0 & 1 & 0 & 0 & 15 & 0 & -3 & -4 & 4 \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{7}{12} & 0 & 0 & 0 & 0 & 0 & 1 & -10 & 0 & -2 & 4 & 0 \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 1 & -\\frac{1}{2} & \\frac{1}{2} & 0 \\\\\n", "{\\color{green}{s}}_{2} & \\frac{11}{48} & 0 & 0 & 0 & 0 & 1 & 0 & 4 & 0 & \\frac{7}{2} & -\\frac{9}{2} & 2 \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{275}{6} & 0 & 0 & 0 & 0 & 0 & 0 & -5 & 0 & -6 & -6 & 198\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7| rhs]\n", "[------+----------------------------------------------------------------------------+------]\n", "[ x4| 1 0 0 1 0 0 0 -2 0 0 1| 5]\n", "[ x3| 23/12 0 1 0 0 0 0 1 0 0 0| 6]\n", "[ x2| 11/16 1 0 0 0 0 0 1 0 1/2 -1/2| 3]\n", "[ s1| 79/24 0 0 0 1 0 0 15 0 -3 -4| 4]\n", "[ s3| -7/12 0 0 0 0 0 1 -10 0 -2 4| 0]\n", "[ s5| 0 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