{ "cells": [ { "cell_type": "code", "execution_count": 6, "id": "a398338b", "metadata": {}, "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": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n", "\\begin{array}{lcrcrcl}\n", " \\max \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 90 x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 100 x_{2} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{2} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 75 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 5 x_{1} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 80 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 4 x_{2} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 60 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 6 x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 10 x_{2} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 354 \\\\\n", "\\end{array} \\\\\n", "x_{1}, x_{2} \\geq 0\n", "\\end{array}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n", "\\begin{array}{lcrcrcl}\n", " \\max \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 90 x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 100 x_{2} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{2} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 75 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 5 x_{1} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 80 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 4 x_{2} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 60 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 6 x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 10 x_{2} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 354 \\\\\n", "\\end{array} \\\\\n", "x_{1}, x_{2} \\geq 0\n", "\\end{array}$$" ], "text/plain": [ "LP problem (use 'view(...)' or '%display typeset' for details)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}4560$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}4560$$" ], "text/plain": [ "4560" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(34,\\,15\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(34,\\,15\\right)$$" ], "text/plain": [ "(34, 15)" ] }, "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": [ "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": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\texttt{El dual es:}}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\texttt{El dual es:}}$$" ], "text/plain": [ "dual" ] }, "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": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n", "\\begin{array}{lcrcrcrcrcl}\n", " \\min \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 75 y_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 80 y_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 60 y_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 354 y_{4} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 5 y_{2} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 6 y_{4} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 90 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{1} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 4 y_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 10 y_{4} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 100 \\\\\n", "\\end{array} \\\\\n", "y_{1} \\geq 0,\\ y_{2} \\leq 0,\\ y_{3} \\leq 0,\\ y_{4} \\geq 0\n", "\\end{array}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n", "\\begin{array}{lcrcrcrcrcl}\n", " \\min \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 75 y_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 80 y_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 60 y_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 354 y_{4} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 5 y_{2} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 6 y_{4} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 90 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{1} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 4 y_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 10 y_{4} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 100 \\\\\n", "\\end{array} \\\\\n", "y_{1} \\geq 0,\\ y_{2} \\leq 0,\\ y_{3} \\leq 0,\\ y_{4} \\geq 0\n", "\\end{array}$$" ], "text/plain": [ "LP problem (use 'view(...)' or '%display typeset' for details)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}4560$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}4560$$" ], "text/plain": [ "4560" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(0,\\,0,\\,-\\frac{25}{2},\\,15\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(0,\\,0,\\,-\\frac{25}{2},\\,15\\right)$$" ], "text/plain": [ "(0, 0, -25/2, 15)" ] }, "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": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\ \\ \\ Fase\\ I}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\ \\ \\ Fase\\ I}$$" ], "text/plain": [ "FI" ] }, "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": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{red}{t}}_{2} & {\\color{red}{t}}_{3} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 75 \\\\\n", "{\\color{red}{t}}_{2} & 5 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 80 \\\\\n", "{\\color{red}{t}}_{3} & 0 & 4 & 0 & 0 & -1 & 0 & 0 & 1 & 60 \\\\\n", "{\\color{green}{s}}_{4} & 6 & 10 & 0 & 0 & 0 & 1 & 0 & 0 & 354 \\\\\n", "\\hline\n", " {W_{ind}} & -5 & -4 & 0 & 1 & 1 & 0 & 0 & 0 & 140\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{red}{t}}_{2} & {\\color{red}{t}}_{3} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 75 \\\\\n", "{\\color{red}{t}}_{2} & 5 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 80 \\\\\n", "{\\color{red}{t}}_{3} & 0 & 4 & 0 & 0 & -1 & 0 & 0 & 1 & 60 \\\\\n", "{\\color{green}{s}}_{4} & 6 & 10 & 0 & 0 & 0 & 1 & 0 & 0 & 354 \\\\\n", "\\hline\n", " {W_{ind}} & -5 & -4 & 0 & 1 & 1 & 0 & 0 & 0 & 140\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 s1 s2 s3 s4 t2 t3|rhs]\n", "[---+-------------------------------+---]\n", "[ s1| 1 1 1 0 0 0 0 0| 75]\n", "[ t2| 5 0 0 -1 0 0 1 0| 80]\n", "[ t3| 0 4 0 0 -1 0 0 1| 60]\n", "[ s4| 6 10 0 0 0 1 0 0|354]\n", "[---+-------------------------------+---]\n", "[ W| -5 -4 0 1 1 0 0 0|140]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 2 , 1 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{red}{t}}_{2} & {\\color{red}{t}}_{3} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 1 & 1 & \\frac{1}{5} & 0 & 0 & -\\frac{1}{5} & 0 & 59 \\\\\n", "{x}_{1} & 1 & 0 & 0 & -\\frac{1}{5} & 0 & 0 & \\frac{1}{5} & 0 & 16 \\\\\n", "{\\color{red}{t}}_{3} & 0 & 4 & 0 & 0 & -1 & 0 & 0 & 1 & 60 \\\\\n", "{\\color{green}{s}}_{4} & 0 & 10 & 0 & \\frac{6}{5} & 0 & 1 & -\\frac{6}{5} & 0 & 258 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & -4 & 0 & 0 & 1 & 0 & 1 & 0 & 60\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{red}{t}}_{2} & {\\color{red}{t}}_{3} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 1 & 1 & \\frac{1}{5} & 0 & 0 & -\\frac{1}{5} & 0 & 59 \\\\\n", "{x}_{1} & 1 & 0 & 0 & -\\frac{1}{5} & 0 & 0 & \\frac{1}{5} & 0 & 16 \\\\\n", "{\\color{red}{t}}_{3} & 0 & 4 & 0 & 0 & -1 & 0 & 0 & 1 & 60 \\\\\n", "{\\color{green}{s}}_{4} & 0 & 10 & 0 & \\frac{6}{5} & 0 & 1 & -\\frac{6}{5} & 0 & 258 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & -4 & 0 & 0 & 1 & 0 & 1 & 0 & 60\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 s1 s2 s3 s4 t2 t3| rhs]\n", "[----+---------------------------------------+----]\n", "[ s1| 0 1 1 1/5 0 0 -1/5 0| 59]\n", "[ x1| 1 0 0 -1/5 0 0 1/5 0| 16]\n", "[ t3| 0 4 0 0 -1 0 0 1| 60]\n", "[ s4| 0 10 0 6/5 0 1 -6/5 0| 258]\n", "[----+---------------------------------------+----]\n", "[ W| 0 -4 0 0 1 0 1 0| 60]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 3 , 2 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{red}{t}}_{2} & {\\color{red}{t}}_{3} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 0 & 1 & \\frac{1}{5} & \\frac{1}{4} & 0 & -\\frac{1}{5} & -\\frac{1}{4} & 44 \\\\\n", "{x}_{1} & 1 & 0 & 0 & -\\frac{1}{5} & 0 & 0 & \\frac{1}{5} & 0 & 16 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & -\\frac{1}{4} & 0 & 0 & \\frac{1}{4} & 15 \\\\\n", "{\\color{green}{s}}_{4} & 0 & 0 & 0 & \\frac{6}{5} & \\frac{5}{2} & 1 & -\\frac{6}{5} & -\\frac{5}{2} & 108 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{red}{t}}_{2} & {\\color{red}{t}}_{3} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 0 & 1 & \\frac{1}{5} & \\frac{1}{4} & 0 & -\\frac{1}{5} & -\\frac{1}{4} & 44 \\\\\n", "{x}_{1} & 1 & 0 & 0 & -\\frac{1}{5} & 0 & 0 & \\frac{1}{5} & 0 & 16 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & -\\frac{1}{4} & 0 & 0 & \\frac{1}{4} & 15 \\\\\n", "{\\color{green}{s}}_{4} & 0 & 0 & 0 & \\frac{6}{5} & \\frac{5}{2} & 1 & -\\frac{6}{5} & -\\frac{5}{2} & 108 \\\\\n", "\\hline\n", " {W_{ind}} & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 s1 s2 s3 s4 t2 t3| rhs]\n", "[----+---------------------------------------+----]\n", "[ s1| 0 0 1 1/5 1/4 0 -1/5 -1/4| 44]\n", "[ x1| 1 0 0 -1/5 0 0 1/5 0| 16]\n", "[ x2| 0 1 0 0 -1/4 0 0 1/4| 15]\n", "[ s4| 0 0 0 6/5 5/2 1 -6/5 -5/2| 108]\n", "[----+---------------------------------------+----]\n", "[ W| 0 0 0 0 0 0 1 1| 0]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "El problema de la fase I es óptimo y Wopt=0. Por tanto, el original es factible\n", "Preparemos el cuadro inicial de la fase II\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": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\ \\ \\ Fase\\ II}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\ \\ \\ Fase\\ II}$$" ], "text/plain": [ "FII" ] }, "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": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 0 & 1 & \\frac{1}{5} & \\frac{1}{4} & 0 & 44 \\\\\n", "{x}_{1} & 1 & 0 & 0 & -\\frac{1}{5} & 0 & 0 & 16 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & -\\frac{1}{4} & 0 & 15 \\\\\n", "{\\color{green}{s}}_{4} & 0 & 0 & 0 & \\frac{6}{5} & \\frac{5}{2} & 1 & 108 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 18 & 25 & 0 & 2940\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 0 & 1 & \\frac{1}{5} & \\frac{1}{4} & 0 & 44 \\\\\n", "{x}_{1} & 1 & 0 & 0 & -\\frac{1}{5} & 0 & 0 & 16 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & -\\frac{1}{4} & 0 & 15 \\\\\n", "{\\color{green}{s}}_{4} & 0 & 0 & 0 & \\frac{6}{5} & \\frac{5}{2} & 1 & 108 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 18 & 25 & 0 & 2940\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 s1 s2 s3 s4| rhs]\n", "[----+-----------------------------+----]\n", "[ s1| 0 0 1 1/5 1/4 0| 44]\n", "[ x1| 1 0 0 -1/5 0 0| 16]\n", "[ x2| 0 1 0 0 -1/4 0| 15]\n", "[ s4| 0 0 0 6/5 5/2 1| 108]\n", "[----+-----------------------------+----]\n", "[ Z| 0 0 0 18 25 0|2940]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 4 , 5 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 0 & 1 & \\frac{2}{25} & 0 & -\\frac{1}{10} & \\frac{166}{5} \\\\\n", "{x}_{1} & 1 & 0 & 0 & -\\frac{1}{5} & 0 & 0 & 16 \\\\\n", "{x}_{2} & 0 & 1 & 0 & \\frac{3}{25} & 0 & \\frac{1}{10} & \\frac{129}{5} \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & \\frac{12}{25} & 1 & \\frac{2}{5} & \\frac{216}{5} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 6 & 0 & -10 & 4020\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 0 & 1 & \\frac{2}{25} & 0 & -\\frac{1}{10} & \\frac{166}{5} \\\\\n", "{x}_{1} & 1 & 0 & 0 & -\\frac{1}{5} & 0 & 0 & 16 \\\\\n", "{x}_{2} & 0 & 1 & 0 & \\frac{3}{25} & 0 & \\frac{1}{10} & \\frac{129}{5} \\\\\n", "{\\color{green}{s}}_{3} & 0 & 0 & 0 & \\frac{12}{25} & 1 & \\frac{2}{5} & \\frac{216}{5} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 6 & 0 & -10 & 4020\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 s1 s2 s3 s4| rhs]\n", "[-----+-----------------------------------+-----]\n", "[ s1| 0 0 1 2/25 0 -1/10|166/5]\n", "[ x1| 1 0 0 -1/5 0 0| 16]\n", "[ x2| 0 1 0 3/25 0 1/10|129/5]\n", "[ s3| 0 0 0 12/25 1 2/5|216/5]\n", "[-----+-----------------------------------+-----]\n", "[ Z| 0 0 0 6 0 -10| 4020]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 4 , 4 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 0 & 1 & 0 & -\\frac{1}{6} & -\\frac{1}{6} & 26 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & \\frac{5}{12} & \\frac{1}{6} & 34 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & -\\frac{1}{4} & 0 & 15 \\\\\n", "{\\color{green}{s}}_{2} & 0 & 0 & 0 & 1 & \\frac{25}{12} & \\frac{5}{6} & 90 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & -\\frac{25}{2} & -15 & 4560\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 0 & 1 & 0 & -\\frac{1}{6} & -\\frac{1}{6} & 26 \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & \\frac{5}{12} & \\frac{1}{6} & 34 \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & -\\frac{1}{4} & 0 & 15 \\\\\n", "{\\color{green}{s}}_{2} & 0 & 0 & 0 & 1 & \\frac{25}{12} & \\frac{5}{6} & 90 \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & -\\frac{25}{2} & -15 & 4560\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 s1 s2 s3 s4| rhs]\n", "[-----+-----------------------------------+-----]\n", "[ s1| 0 0 1 0 -1/6 -1/6| 26]\n", "[ x1| 1 0 0 0 5/12 1/6| 34]\n", "[ x2| 0 1 0 0 -1/4 0| 15]\n", "[ s2| 0 0 0 1 25/12 5/6| 90]\n", "[-----+-----------------------------------+-----]\n", "[ Z| 0 0 0 0 -25/2 -15| 4560]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "El problema es óptimo\n" ] } ], "source": [ "tipo='max' # max o min\n", "\n", "n=2 # número de variables x's\n", "m=4 # número de restricciones (distintas de las de signo)\n", "\n", "c=matrix(QQ,1,n,[90,100] ) # vector de costos\n", "\n", "A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n", "[1,1],\n", "[5,0],\n", "[0,4],\n", "[6,10]\n", "])\n", "\n", "b=matrix(QQ,m,1,[75,80,60,354]) # vector de la derecha\n", "\n", "\n", "######################################################\n", "############### VARIABLES DE HOLGURA ################\n", "\n", "\n", "h=matrix(ZZ,1,m,[1,-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", "####################################################################\n", "############ HASTA AQUÍ LOS DATOS ################################\n", "####################################################################\n", "\n", "\n", "load('https://sage.unex.es/501708/simplex2023Auto.sage')\n", "#load('https://sage.unex.es/501708/simplex2023AutoREVISED.sage')\n", "#load('https://sage.unex.es/501708/simplex2023CompletamenteManual.sage')\n", "\n" ] }, { "cell_type": "code", "execution_count": 7, "id": "3e455866", "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrrr}\n", "1 & 0 & \\frac{1}{6} & -\\frac{1}{6} \\\\\n", "0 & 0 & -\\frac{5}{12} & \\frac{1}{6} \\\\\n", "0 & 0 & \\frac{1}{4} & 0 \\\\\n", "0 & -1 & -\\frac{25}{12} & \\frac{5}{6}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrrr}\n", "1 & 0 & \\frac{1}{6} & -\\frac{1}{6} \\\\\n", "0 & 0 & -\\frac{5}{12} & \\frac{1}{6} \\\\\n", "0 & 0 & \\frac{1}{4} & 0 \\\\\n", "0 & -1 & -\\frac{25}{12} & \\frac{5}{6}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ 1 0 1/6 -1/6]\n", "[ 0 0 -5/12 1/6]\n", "[ 0 0 1/4 0]\n", "[ 0 -1 -25/12 5/6]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(BM1)" ] }, { "cell_type": "code", "execution_count": 8, "id": "c296dac0", "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrr|rr}\n", "{Basic} & {x}_{1} & {x}_{2} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} & {b_1} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 0 & 1 & 0 & -\\frac{1}{6} & -\\frac{1}{6} & 26 & -\\frac{4}{3} \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & \\frac{5}{12} & \\frac{1}{6} & 34 & \\frac{7}{12} \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & -\\frac{1}{4} & 0 & 15 & -\\frac{1}{4} \\\\\n", "{\\color{green}{s}}_{2} & 0 & 0 & 0 & 1 & \\frac{25}{12} & \\frac{5}{6} & 90 & \\frac{23}{12} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & -\\frac{25}{2} & -15 & 4560 & \\frac{55}{2}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrr|rr}\n", "{Basic} & {x}_{1} & {x}_{2} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} & {b_1} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 0 & 0 & 1 & 0 & -\\frac{1}{6} & -\\frac{1}{6} & 26 & -\\frac{4}{3} \\\\\n", "{x}_{1} & 1 & 0 & 0 & 0 & \\frac{5}{12} & \\frac{1}{6} & 34 & \\frac{7}{12} \\\\\n", "{x}_{2} & 0 & 1 & 0 & 0 & -\\frac{1}{4} & 0 & 15 & -\\frac{1}{4} \\\\\n", "{\\color{green}{s}}_{2} & 0 & 0 & 0 & 1 & \\frac{25}{12} & \\frac{5}{6} & 90 & \\frac{23}{12} \\\\\n", "\\hline\n", " {Z_{ind}} & 0 & 0 & 0 & 0 & -\\frac{25}{2} & -15 & 4560 & \\frac{55}{2}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 s1 s2 s3 s4| rhs rhs1]\n", "[-----+-----------------------------------+-----------]\n", "[ s1| 0 0 1 0 -1/6 -1/6| 26 -4/3]\n", "[ x1| 1 0 0 0 5/12 1/6| 34 7/12]\n", "[ x2| 0 1 0 0 -1/4 0| 15 -1/4]\n", "[ s2| 0 0 0 1 25/12 5/6| 90 23/12]\n", "[-----+-----------------------------------+-----------]\n", "[ Z| 0 0 0 0 -25/2 -15| 4560 55/2]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "bp=matrix(QQ,m,1,[-1,1,-1,1]); param1b(bp) " ] }, { "cell_type": "code", "execution_count": null, "id": "b79e6d44", "metadata": {}, "outputs": [], "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": 5 }