{ "cells": [ { "cell_type": "code", "execution_count": 30, "id": "cc483fa5", "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": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n", "\\begin{array}{lcrcrcrcrcl}\n", " \\max \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{2} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 3 x_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{4} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 10 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 12 x_{3} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 8 x_{4} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 24 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 6 x_{1} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 4 x_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 5 x_{4} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 52 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 6 x_{2} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 4 x_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 3 x_{4} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 17 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 2 x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 10 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{3} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 5 x_{4} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 18 \\\\\n", "\\end{array} \\\\\n", "x_{1}, x_{2}, x_{3}, x_{4} \\geq 0\n", "\\end{array}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n", "\\begin{array}{lcrcrcrcrcl}\n", " \\max \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{2} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 3 x_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{4} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 10 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 12 x_{3} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 8 x_{4} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 24 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 6 x_{1} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 4 x_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 5 x_{4} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 52 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 6 x_{2} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 4 x_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 3 x_{4} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 17 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 2 x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 10 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{3} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 5 x_{4} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 18 \\\\\n", "\\end{array} \\\\\n", "x_{1}, x_{2}, x_{3}, x_{4} \\geq 0\n", "\\end{array}$$" ], "text/plain": [ "LP problem (use 'view(...)' or '%display typeset' for details)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{174}{5}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{174}{5}$$" ], "text/plain": [ "174/5" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(0,\\,7,\\,0,\\,\\frac{52}{5}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(0,\\,7,\\,0,\\,\\frac{52}{5}\\right)$$" ], "text/plain": [ "(0, 7, 0, 52/5)" ] }, "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": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n", "\\begin{array}{lcrcrcrcrcl}\n", " \\min \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 24 y_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 52 y_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 17 y_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 18 y_{4} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 6 y_{2} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 2 y_{4} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} -1 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 10 y_{1} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 6 y_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 10 y_{4} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 2 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 12 y_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 4 y_{2} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 4 y_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 y_{4} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} -3 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 8 y_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 5 y_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 3 y_{3} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 5 y_{4} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 2 \\\\\n", "\\end{array} \\\\\n", "y_{1}, y_{2}, y_{3}, y_{4} \\geq 0\n", "\\end{array}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n", "\\begin{array}{lcrcrcrcrcl}\n", " \\min \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 24 y_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 52 y_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 17 y_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 18 y_{4} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} y_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 6 y_{2} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 2 y_{4} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} -1 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 10 y_{1} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 6 y_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 10 y_{4} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 2 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} \\mspace{-6mu}&\\mspace{-6mu} 12 y_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 4 y_{2} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 4 y_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 y_{4} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} -3 \\\\\n", " \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 8 y_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 5 y_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 3 y_{3} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 5 y_{4} \\mspace{-6mu}&\\mspace{-6mu} \\geq \\mspace{-6mu}&\\mspace{-6mu} 2 \\\\\n", "\\end{array} \\\\\n", "y_{1}, y_{2}, y_{3}, y_{4} \\geq 0\n", "\\end{array}$$" ], "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": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{174}{5}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{174}{5}$$" ], "text/plain": [ "174/5" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(0,\\,\\frac{3}{5},\\,0,\\,\\frac{1}{5}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(0,\\,\\frac{3}{5},\\,0,\\,\\frac{1}{5}\\right)$$" ], "text/plain": [ "(0, 3/5, 0, 1/5)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{}$$" ], "text/plain": [ "salto" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{===================================}$$" ], "text/plain": [ "ry" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 1 & 10 & 12 & -8 & 1 & 0 & 0 & 0 & 24 \\\\\n", "{\\color{green}{s}}_{2} & 6 & 0 & 4 & 5 & 0 & 1 & 0 & 0 & 52 \\\\\n", "{\\color{green}{s}}_{3} & 0 & -6 & -4 & 3 & 0 & 0 & 1 & 0 & 17 \\\\\n", "{\\color{green}{s}}_{4} & -2 & 10 & 2 & -5 & 0 & 0 & 0 & 1 & 18 \\\\\n", "\\hline\n", " {Z_{ind}} & -1 & 2 & -3 & 2 & 0 & 0 & 0 & 0 & 0\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 1 & 10 & 12 & -8 & 1 & 0 & 0 & 0 & 24 \\\\\n", "{\\color{green}{s}}_{2} & 6 & 0 & 4 & 5 & 0 & 1 & 0 & 0 & 52 \\\\\n", "{\\color{green}{s}}_{3} & 0 & -6 & -4 & 3 & 0 & 0 & 1 & 0 & 17 \\\\\n", "{\\color{green}{s}}_{4} & -2 & 10 & 2 & -5 & 0 & 0 & 0 & 1 & 18 \\\\\n", "\\hline\n", " {Z_{ind}} & -1 & 2 & -3 & 2 & 0 & 0 & 0 & 0 & 0\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4|rhs]\n", "[---+-------------------------------+---]\n", "[ s1| 1 10 12 -8 1 0 0 0| 24]\n", "[ s2| 6 0 4 5 0 1 0 0| 52]\n", "[ s3| 0 -6 -4 3 0 0 1 0| 17]\n", "[ s4| -2 10 2 -5 0 0 0 1| 18]\n", "[---+-------------------------------+---]\n", "[ Z| -1 2 -3 2 0 0 0 0| 0]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 4 , 2 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 3 & 0 & 10 & -3 & 1 & 0 & 0 & -1 & 6 \\\\\n", "{\\color{green}{s}}_{2} & 6 & 0 & 4 & 5 & 0 & 1 & 0 & 0 & 52 \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{6}{5} & 0 & -\\frac{14}{5} & 0 & 0 & 0 & 1 & \\frac{3}{5} & \\frac{139}{5} \\\\\n", "{x}_{2} & -\\frac{1}{5} & 1 & \\frac{1}{5} & -\\frac{1}{2} & 0 & 0 & 0 & \\frac{1}{10} & \\frac{9}{5} \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{3}{5} & 0 & -\\frac{17}{5} & 3 & 0 & 0 & 0 & -\\frac{1}{5} & \\frac{18}{5}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 3 & 0 & 10 & -3 & 1 & 0 & 0 & -1 & 6 \\\\\n", "{\\color{green}{s}}_{2} & 6 & 0 & 4 & 5 & 0 & 1 & 0 & 0 & 52 \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{6}{5} & 0 & -\\frac{14}{5} & 0 & 0 & 0 & 1 & \\frac{3}{5} & \\frac{139}{5} \\\\\n", "{x}_{2} & -\\frac{1}{5} & 1 & \\frac{1}{5} & -\\frac{1}{2} & 0 & 0 & 0 & \\frac{1}{10} & \\frac{9}{5} \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{3}{5} & 0 & -\\frac{17}{5} & 3 & 0 & 0 & 0 & -\\frac{1}{5} & \\frac{18}{5}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4| rhs]\n", "[-----+-----------------------------------------------+-----]\n", "[ s1| 3 0 10 -3 1 0 0 -1| 6]\n", "[ s2| 6 0 4 5 0 1 0 0| 52]\n", "[ s3| -6/5 0 -14/5 0 0 0 1 3/5|139/5]\n", "[ x2| -1/5 1 1/5 -1/2 0 0 0 1/10| 9/5]\n", "[-----+-----------------------------------------------+-----]\n", "[ Z| -3/5 0 -17/5 3 0 0 0 -1/5| 18/5]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "cambio( 2 , 4 )\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & \\frac{33}{5} & 0 & \\frac{62}{5} & 0 & 1 & \\frac{3}{5} & 0 & -1 & \\frac{186}{5} \\\\\n", "{x}_{4} & \\frac{6}{5} & 0 & \\frac{4}{5} & 1 & 0 & \\frac{1}{5} & 0 & 0 & \\frac{52}{5} \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{6}{5} & 0 & -\\frac{14}{5} & 0 & 0 & 0 & 1 & \\frac{3}{5} & \\frac{139}{5} \\\\\n", "{x}_{2} & \\frac{2}{5} & 1 & \\frac{3}{5} & 0 & 0 & \\frac{1}{10} & 0 & \\frac{1}{10} & 7 \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{21}{5} & 0 & -\\frac{29}{5} & 0 & 0 & -\\frac{3}{5} & 0 & -\\frac{1}{5} & \\frac{174}{5}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & \\frac{33}{5} & 0 & \\frac{62}{5} & 0 & 1 & \\frac{3}{5} & 0 & -1 & \\frac{186}{5} \\\\\n", "{x}_{4} & \\frac{6}{5} & 0 & \\frac{4}{5} & 1 & 0 & \\frac{1}{5} & 0 & 0 & \\frac{52}{5} \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{6}{5} & 0 & -\\frac{14}{5} & 0 & 0 & 0 & 1 & \\frac{3}{5} & \\frac{139}{5} \\\\\n", "{x}_{2} & \\frac{2}{5} & 1 & \\frac{3}{5} & 0 & 0 & \\frac{1}{10} & 0 & \\frac{1}{10} & 7 \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{21}{5} & 0 & -\\frac{29}{5} & 0 & 0 & -\\frac{3}{5} & 0 & -\\frac{1}{5} & \\frac{174}{5}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4| rhs]\n", "[-----+-----------------------------------------------+-----]\n", "[ s1| 33/5 0 62/5 0 1 3/5 0 -1|186/5]\n", "[ x4| 6/5 0 4/5 1 0 1/5 0 0| 52/5]\n", "[ s3| -6/5 0 -14/5 0 0 0 1 3/5|139/5]\n", "[ x2| 2/5 1 3/5 0 0 1/10 0 1/10| 7]\n", "[-----+-----------------------------------------------+-----]\n", "[ Z|-21/5 0 -29/5 0 0 -3/5 0 -1/5|174/5]" ] }, "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=4 # número de variables x's\n", "m=4 # número de restricciones (distintas de las de signo)\n", "\n", "c=matrix(QQ,1,n,[-1,2,-3,2] ) # vector de costos\n", "\n", "\n", "\n", "A=matrix(QQ,m,n,[ # coeficientes de las variables x's\n", "[1,10,12,-8],\n", "[6,0,4,5],\n", "[0,-6,-4,3],\n", "[-2,10,2,-5]\n", "])\n", "\n", "\n", "Aori=A\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "b=matrix(QQ,m,1,[24,52,17,18]) # vector de la derecha\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", "#t=matrix(ZZ,1,m,[0,0,0,0]) # variables artificiales: \n", " # pon 1 si utilizas variable artificial en la fila i-ésima\n", " # 0 si no utilizas variable artificial en la fila i-ésima\n", "\n", "#colId=(1,2,3,4) # posición de la matriz identidad\n", "\n", "\n", " \n", " \n", "####################################################################\n", "############ HASTA AQUÍ LOS DATOS ################################\n", "####################################################################\n", "\n", "\n", "load('https://sage.unex.es/501708/simplex2023Auto.sage')\n", "\n", "#load('https://sage.unex.es/501708/simplex2023CompletamenteManual.sage')\n" ] }, { "cell_type": "markdown", "id": "55209452", "metadata": {}, "source": [ "introduciendo x0 como la variable z y poniendo la ecuación que define a la z en la primera fila, resulta que todos los vectores columnas con léxico positivos. Aquí no haremos esos cambios" ] }, { "cell_type": "code", "execution_count": 31, "id": "f173b9ef", "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[1, 2, 3, 4, 5, 6, 7, 8\\right]$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[1, 2, 3, 4, 5, 6, 7, 8\\right]$$" ], "text/plain": [ "[1, 2, 3, 4, 5, 6, 7, 8]" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & \\frac{33}{5} & 0 & \\frac{62}{5} & 0 & 1 & \\frac{3}{5} & 0 & -1 & 0 & \\frac{186}{5} \\\\\n", "{x}_{4} & \\frac{6}{5} & 0 & \\frac{4}{5} & 1 & 0 & \\frac{1}{5} & 0 & 0 & 0 & \\frac{52}{5} \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{6}{5} & 0 & -\\frac{14}{5} & 0 & 0 & 0 & 1 & \\frac{3}{5} & 0 & \\frac{139}{5} \\\\\n", "{x}_{2} & \\frac{2}{5} & 1 & \\frac{3}{5} & 0 & 0 & \\frac{1}{10} & 0 & \\frac{1}{10} & 0 & 7 \\\\\n", "{\\color{green}{s}}_{5} & -2 & 0 & -3 & 0 & 0 & -2 & 0 & 0 & 1 & -4 \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{21}{5} & 0 & -\\frac{29}{5} & 0 & 0 & -\\frac{3}{5} & 0 & -\\frac{1}{5} & 0 & \\frac{174}{5}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & \\frac{33}{5} & 0 & \\frac{62}{5} & 0 & 1 & \\frac{3}{5} & 0 & -1 & 0 & \\frac{186}{5} \\\\\n", "{x}_{4} & \\frac{6}{5} & 0 & \\frac{4}{5} & 1 & 0 & \\frac{1}{5} & 0 & 0 & 0 & \\frac{52}{5} \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{6}{5} & 0 & -\\frac{14}{5} & 0 & 0 & 0 & 1 & \\frac{3}{5} & 0 & \\frac{139}{5} \\\\\n", "{x}_{2} & \\frac{2}{5} & 1 & \\frac{3}{5} & 0 & 0 & \\frac{1}{10} & 0 & \\frac{1}{10} & 0 & 7 \\\\\n", "{\\color{green}{s}}_{5} & -2 & 0 & -3 & 0 & 0 & -2 & 0 & 0 & 1 & -4 \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{21}{5} & 0 & -\\frac{29}{5} & 0 & 0 & -\\frac{3}{5} & 0 & -\\frac{1}{5} & 0 & \\frac{174}{5}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5| rhs]\n", "[-----+-----------------------------------------------------+-----]\n", "[ s1| 33/5 0 62/5 0 1 3/5 0 -1 0|186/5]\n", "[ x4| 6/5 0 4/5 1 0 1/5 0 0 0| 52/5]\n", "[ s3| -6/5 0 -14/5 0 0 0 1 3/5 0|139/5]\n", "[ x2| 2/5 1 3/5 0 0 1/10 0 1/10 0| 7]\n", "[ s5| -2 0 -3 0 0 -2 0 0 1| -4]\n", "[-----+-----------------------------------------------------+-----]\n", "[ Z|-21/5 0 -29/5 0 0 -3/5 0 -1/5 0|174/5]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "corte(1)" ] }, { "cell_type": "code", "execution_count": 32, "id": "0590fad4", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[ 2.1000 NO 1.9333 NO NO 0.30000 NO NO NO]" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cocientesD(5)" ] }, { "cell_type": "code", "execution_count": 33, "id": "347a3577", "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 6 & 0 & \\frac{23}{2} & 0 & 1 & 0 & 0 & -1 & \\frac{3}{10} & 36 \\\\\n", "{x}_{4} & 1 & 0 & \\frac{1}{2} & 1 & 0 & 0 & 0 & 0 & \\frac{1}{10} & 10 \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{6}{5} & 0 & -\\frac{14}{5} & 0 & 0 & 0 & 1 & \\frac{3}{5} & 0 & \\frac{139}{5} \\\\\n", "{x}_{2} & \\frac{3}{10} & 1 & \\frac{9}{20} & 0 & 0 & 0 & 0 & \\frac{1}{10} & \\frac{1}{20} & \\frac{34}{5} \\\\\n", "{\\color{green}{s}}_{2} & 1 & 0 & \\frac{3}{2} & 0 & 0 & 1 & 0 & 0 & -\\frac{1}{2} & 2 \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{18}{5} & 0 & -\\frac{49}{10} & 0 & 0 & 0 & 0 & -\\frac{1}{5} & -\\frac{3}{10} & \\frac{168}{5}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 6 & 0 & \\frac{23}{2} & 0 & 1 & 0 & 0 & -1 & \\frac{3}{10} & 36 \\\\\n", "{x}_{4} & 1 & 0 & \\frac{1}{2} & 1 & 0 & 0 & 0 & 0 & \\frac{1}{10} & 10 \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{6}{5} & 0 & -\\frac{14}{5} & 0 & 0 & 0 & 1 & \\frac{3}{5} & 0 & \\frac{139}{5} \\\\\n", "{x}_{2} & \\frac{3}{10} & 1 & \\frac{9}{20} & 0 & 0 & 0 & 0 & \\frac{1}{10} & \\frac{1}{20} & \\frac{34}{5} \\\\\n", "{\\color{green}{s}}_{2} & 1 & 0 & \\frac{3}{2} & 0 & 0 & 1 & 0 & 0 & -\\frac{1}{2} & 2 \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{18}{5} & 0 & -\\frac{49}{10} & 0 & 0 & 0 & 0 & -\\frac{1}{5} & -\\frac{3}{10} & \\frac{168}{5}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5| rhs]\n", "[------+--------------------------------------------------------------+------]\n", "[ s1| 6 0 23/2 0 1 0 0 -1 3/10| 36]\n", "[ x4| 1 0 1/2 1 0 0 0 0 1/10| 10]\n", "[ s3| -6/5 0 -14/5 0 0 0 1 3/5 0| 139/5]\n", "[ x2| 3/10 1 9/20 0 0 0 0 1/10 1/20| 34/5]\n", "[ s2| 1 0 3/2 0 0 1 0 0 -1/2| 2]\n", "[------+--------------------------------------------------------------+------]\n", "[ Z| -18/5 0 -49/10 0 0 0 0 -1/5 -3/10| 168/5]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(5,6)" ] }, { "cell_type": "code", "execution_count": 34, "id": "80a12600", "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[1, 2, 3, 4, 5, 6, 7, 8, 9\\right]$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[1, 2, 3, 4, 5, 6, 7, 8, 9\\right]$$" ], "text/plain": [ "[1, 2, 3, 4, 5, 6, 7, 8, 9]" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 6 & 0 & \\frac{23}{2} & 0 & 1 & 0 & 0 & -1 & \\frac{3}{10} & 0 & 36 \\\\\n", "{x}_{4} & 1 & 0 & \\frac{1}{2} & 1 & 0 & 0 & 0 & 0 & \\frac{1}{10} & 0 & 10 \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{6}{5} & 0 & -\\frac{14}{5} & 0 & 0 & 0 & 1 & \\frac{3}{5} & 0 & 0 & \\frac{139}{5} \\\\\n", "{x}_{2} & \\frac{3}{10} & 1 & \\frac{9}{20} & 0 & 0 & 0 & 0 & \\frac{1}{10} & \\frac{1}{20} & 0 & \\frac{34}{5} \\\\\n", "{\\color{green}{s}}_{2} & 1 & 0 & \\frac{3}{2} & 0 & 0 & 1 & 0 & 0 & -\\frac{1}{2} & 0 & 2 \\\\\n", "{\\color{green}{s}}_{6} & -4 & 0 & -1 & 0 & 0 & 0 & 0 & -3 & 0 & 1 & -4 \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{18}{5} & 0 & -\\frac{49}{10} & 0 & 0 & 0 & 0 & -\\frac{1}{5} & -\\frac{3}{10} & 0 & \\frac{168}{5}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 6 & 0 & \\frac{23}{2} & 0 & 1 & 0 & 0 & -1 & \\frac{3}{10} & 0 & 36 \\\\\n", "{x}_{4} & 1 & 0 & \\frac{1}{2} & 1 & 0 & 0 & 0 & 0 & \\frac{1}{10} & 0 & 10 \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{6}{5} & 0 & -\\frac{14}{5} & 0 & 0 & 0 & 1 & \\frac{3}{5} & 0 & 0 & \\frac{139}{5} \\\\\n", "{x}_{2} & \\frac{3}{10} & 1 & \\frac{9}{20} & 0 & 0 & 0 & 0 & \\frac{1}{10} & \\frac{1}{20} & 0 & \\frac{34}{5} \\\\\n", "{\\color{green}{s}}_{2} & 1 & 0 & \\frac{3}{2} & 0 & 0 & 1 & 0 & 0 & -\\frac{1}{2} & 0 & 2 \\\\\n", "{\\color{green}{s}}_{6} & -4 & 0 & -1 & 0 & 0 & 0 & 0 & -3 & 0 & 1 & -4 \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{18}{5} & 0 & -\\frac{49}{10} & 0 & 0 & 0 & 0 & -\\frac{1}{5} & -\\frac{3}{10} & 0 & \\frac{168}{5}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n", "[------+---------------------------------------------------------------------+------]\n", "[ s1| 6 0 23/2 0 1 0 0 -1 3/10 0| 36]\n", "[ x4| 1 0 1/2 1 0 0 0 0 1/10 0| 10]\n", "[ s3| -6/5 0 -14/5 0 0 0 1 3/5 0 0| 139/5]\n", "[ x2| 3/10 1 9/20 0 0 0 0 1/10 1/20 0| 34/5]\n", "[ s2| 1 0 3/2 0 0 1 0 0 -1/2 0| 2]\n", "[ s6| -4 0 -1 0 0 0 0 -3 0 1| -4]\n", "[------+---------------------------------------------------------------------+------]\n", "[ Z| -18/5 0 -49/10 0 0 0 0 -1/5 -3/10 0| 168/5]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "corte(3)" ] }, { "cell_type": "code", "execution_count": 35, "id": "c3f090d5", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[ 0.90000 NO 4.9000 NO NO NO NO 0.066667 NO NO]" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cocientesD(6)" ] }, { "cell_type": "code", "execution_count": 36, "id": "de3c81fe", "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & \\frac{22}{3} & 0 & \\frac{71}{6} & 0 & 1 & 0 & 0 & 0 & \\frac{3}{10} & -\\frac{1}{3} & \\frac{112}{3} \\\\\n", "{x}_{4} & 1 & 0 & \\frac{1}{2} & 1 & 0 & 0 & 0 & 0 & \\frac{1}{10} & 0 & 10 \\\\\n", "{\\color{green}{s}}_{3} & -2 & 0 & -3 & 0 & 0 & 0 & 1 & 0 & 0 & \\frac{1}{5} & 27 \\\\\n", "{x}_{2} & \\frac{1}{6} & 1 & \\frac{5}{12} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{20} & \\frac{1}{30} & \\frac{20}{3} \\\\\n", "{\\color{green}{s}}_{2} & 1 & 0 & \\frac{3}{2} & 0 & 0 & 1 & 0 & 0 & -\\frac{1}{2} & 0 & 2 \\\\\n", "{\\color{green}{s}}_{4} & \\frac{4}{3} & 0 & \\frac{1}{3} & 0 & 0 & 0 & 0 & 1 & 0 & -\\frac{1}{3} & \\frac{4}{3} \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{10}{3} & 0 & -\\frac{29}{6} & 0 & 0 & 0 & 0 & 0 & -\\frac{3}{10} & -\\frac{1}{15} & \\frac{100}{3}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & \\frac{22}{3} & 0 & \\frac{71}{6} & 0 & 1 & 0 & 0 & 0 & \\frac{3}{10} & -\\frac{1}{3} & \\frac{112}{3} \\\\\n", "{x}_{4} & 1 & 0 & \\frac{1}{2} & 1 & 0 & 0 & 0 & 0 & \\frac{1}{10} & 0 & 10 \\\\\n", "{\\color{green}{s}}_{3} & -2 & 0 & -3 & 0 & 0 & 0 & 1 & 0 & 0 & \\frac{1}{5} & 27 \\\\\n", "{x}_{2} & \\frac{1}{6} & 1 & \\frac{5}{12} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{20} & \\frac{1}{30} & \\frac{20}{3} \\\\\n", "{\\color{green}{s}}_{2} & 1 & 0 & \\frac{3}{2} & 0 & 0 & 1 & 0 & 0 & -\\frac{1}{2} & 0 & 2 \\\\\n", "{\\color{green}{s}}_{4} & \\frac{4}{3} & 0 & \\frac{1}{3} & 0 & 0 & 0 & 0 & 1 & 0 & -\\frac{1}{3} & \\frac{4}{3} \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{10}{3} & 0 & -\\frac{29}{6} & 0 & 0 & 0 & 0 & 0 & -\\frac{3}{10} & -\\frac{1}{15} & \\frac{100}{3}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6| rhs]\n", "[-----+-----------------------------------------------------------+-----]\n", "[ s1| 22/3 0 71/6 0 1 0 0 0 3/10 -1/3|112/3]\n", "[ x4| 1 0 1/2 1 0 0 0 0 1/10 0| 10]\n", "[ s3| -2 0 -3 0 0 0 1 0 0 1/5| 27]\n", "[ x2| 1/6 1 5/12 0 0 0 0 0 1/20 1/30| 20/3]\n", "[ s2| 1 0 3/2 0 0 1 0 0 -1/2 0| 2]\n", "[ s4| 4/3 0 1/3 0 0 0 0 1 0 -1/3| 4/3]\n", "[-----+-----------------------------------------------------------+-----]\n", "[ Z|-10/3 0 -29/6 0 0 0 0 0 -3/10 -1/15|100/3]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(6,8)" ] }, { "cell_type": "code", "execution_count": 37, "id": "34ae5df4", "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[1, 2, 3, 4, 5, 6, 7, 8, 9, 10\\right]$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[1, 2, 3, 4, 5, 6, 7, 8, 9, 10\\right]$$" ], "text/plain": [ "[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & \\frac{22}{3} & 0 & \\frac{71}{6} & 0 & 1 & 0 & 0 & 0 & \\frac{3}{10} & -\\frac{1}{3} & 0 & \\frac{112}{3} \\\\\n", "{x}_{4} & 1 & 0 & \\frac{1}{2} & 1 & 0 & 0 & 0 & 0 & \\frac{1}{10} & 0 & 0 & 10 \\\\\n", "{\\color{green}{s}}_{3} & -2 & 0 & -3 & 0 & 0 & 0 & 1 & 0 & 0 & \\frac{1}{5} & 0 & 27 \\\\\n", "{x}_{2} & \\frac{1}{6} & 1 & \\frac{5}{12} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{20} & \\frac{1}{30} & 0 & \\frac{20}{3} \\\\\n", "{\\color{green}{s}}_{2} & 1 & 0 & \\frac{3}{2} & 0 & 0 & 1 & 0 & 0 & -\\frac{1}{2} & 0 & 0 & 2 \\\\\n", "{\\color{green}{s}}_{4} & \\frac{4}{3} & 0 & \\frac{1}{3} & 0 & 0 & 0 & 0 & 1 & 0 & -\\frac{1}{3} & 0 & \\frac{4}{3} \\\\\n", "{\\color{green}{s}}_{7} & -20 & 0 & -5 & 0 & 0 & 0 & 0 & 0 & -18 & -10 & 1 & -20 \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{10}{3} & 0 & -\\frac{29}{6} & 0 & 0 & 0 & 0 & 0 & -\\frac{3}{10} & -\\frac{1}{15} & 0 & \\frac{100}{3}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & \\frac{22}{3} & 0 & \\frac{71}{6} & 0 & 1 & 0 & 0 & 0 & \\frac{3}{10} & -\\frac{1}{3} & 0 & \\frac{112}{3} \\\\\n", "{x}_{4} & 1 & 0 & \\frac{1}{2} & 1 & 0 & 0 & 0 & 0 & \\frac{1}{10} & 0 & 0 & 10 \\\\\n", "{\\color{green}{s}}_{3} & -2 & 0 & -3 & 0 & 0 & 0 & 1 & 0 & 0 & \\frac{1}{5} & 0 & 27 \\\\\n", "{x}_{2} & \\frac{1}{6} & 1 & \\frac{5}{12} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{20} & \\frac{1}{30} & 0 & \\frac{20}{3} \\\\\n", "{\\color{green}{s}}_{2} & 1 & 0 & \\frac{3}{2} & 0 & 0 & 1 & 0 & 0 & -\\frac{1}{2} & 0 & 0 & 2 \\\\\n", "{\\color{green}{s}}_{4} & \\frac{4}{3} & 0 & \\frac{1}{3} & 0 & 0 & 0 & 0 & 1 & 0 & -\\frac{1}{3} & 0 & \\frac{4}{3} \\\\\n", "{\\color{green}{s}}_{7} & -20 & 0 & -5 & 0 & 0 & 0 & 0 & 0 & -18 & -10 & 1 & -20 \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{10}{3} & 0 & -\\frac{29}{6} & 0 & 0 & 0 & 0 & 0 & -\\frac{3}{10} & -\\frac{1}{15} & 0 & \\frac{100}{3}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7| rhs]\n", "[-----+-----------------------------------------------------------------+-----]\n", "[ s1| 22/3 0 71/6 0 1 0 0 0 3/10 -1/3 0|112/3]\n", "[ x4| 1 0 1/2 1 0 0 0 0 1/10 0 0| 10]\n", "[ s3| -2 0 -3 0 0 0 1 0 0 1/5 0| 27]\n", "[ x2| 1/6 1 5/12 0 0 0 0 0 1/20 1/30 0| 20/3]\n", "[ s2| 1 0 3/2 0 0 1 0 0 -1/2 0 0| 2]\n", "[ s4| 4/3 0 1/3 0 0 0 0 1 0 -1/3 0| 4/3]\n", "[ s7| -20 0 -5 0 0 0 0 0 -18 -10 1| -20]\n", "[-----+-----------------------------------------------------------------+-----]\n", "[ Z|-10/3 0 -29/6 0 0 0 0 0 -3/10 -1/15 0|100/3]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "corte(1)" ] }, { "cell_type": "code", "execution_count": 38, "id": "6bcab603", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[ 0.16667 NO 0.96667 NO NO NO NO NO 0.016667 0.0066667 NO]" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cocientesD(7)" ] }, { "cell_type": "code", "execution_count": 39, "id": "d266fe47", "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 8 & 0 & 12 & 0 & 1 & 0 & 0 & 0 & \\frac{9}{10} & 0 & -\\frac{1}{30} & 38 \\\\\n", "{x}_{4} & 1 & 0 & \\frac{1}{2} & 1 & 0 & 0 & 0 & 0 & \\frac{1}{10} & 0 & 0 & 10 \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{12}{5} & 0 & -\\frac{31}{10} & 0 & 0 & 0 & 1 & 0 & -\\frac{9}{25} & 0 & \\frac{1}{50} & \\frac{133}{5} \\\\\n", "{x}_{2} & \\frac{1}{10} & 1 & \\frac{2}{5} & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{100} & 0 & \\frac{1}{300} & \\frac{33}{5} \\\\\n", "{\\color{green}{s}}_{2} & 1 & 0 & \\frac{3}{2} & 0 & 0 & 1 & 0 & 0 & -\\frac{1}{2} & 0 & 0 & 2 \\\\\n", "{\\color{green}{s}}_{4} & 2 & 0 & \\frac{1}{2} & 0 & 0 & 0 & 0 & 1 & \\frac{3}{5} & 0 & -\\frac{1}{30} & 2 \\\\\n", "{\\color{green}{s}}_{6} & 2 & 0 & \\frac{1}{2} & 0 & 0 & 0 & 0 & 0 & \\frac{9}{5} & 1 & -\\frac{1}{10} & 2 \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{16}{5} & 0 & -\\frac{24}{5} & 0 & 0 & 0 & 0 & 0 & -\\frac{9}{50} & 0 & -\\frac{1}{150} & \\frac{166}{5}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 8 & 0 & 12 & 0 & 1 & 0 & 0 & 0 & \\frac{9}{10} & 0 & -\\frac{1}{30} & 38 \\\\\n", "{x}_{4} & 1 & 0 & \\frac{1}{2} & 1 & 0 & 0 & 0 & 0 & \\frac{1}{10} & 0 & 0 & 10 \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{12}{5} & 0 & -\\frac{31}{10} & 0 & 0 & 0 & 1 & 0 & -\\frac{9}{25} & 0 & \\frac{1}{50} & \\frac{133}{5} \\\\\n", "{x}_{2} & \\frac{1}{10} & 1 & \\frac{2}{5} & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{100} & 0 & \\frac{1}{300} & \\frac{33}{5} \\\\\n", "{\\color{green}{s}}_{2} & 1 & 0 & \\frac{3}{2} & 0 & 0 & 1 & 0 & 0 & -\\frac{1}{2} & 0 & 0 & 2 \\\\\n", "{\\color{green}{s}}_{4} & 2 & 0 & \\frac{1}{2} & 0 & 0 & 0 & 0 & 1 & \\frac{3}{5} & 0 & -\\frac{1}{30} & 2 \\\\\n", "{\\color{green}{s}}_{6} & 2 & 0 & \\frac{1}{2} & 0 & 0 & 0 & 0 & 0 & \\frac{9}{5} & 1 & -\\frac{1}{10} & 2 \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{16}{5} & 0 & -\\frac{24}{5} & 0 & 0 & 0 & 0 & 0 & -\\frac{9}{50} & 0 & -\\frac{1}{150} & \\frac{166}{5}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7| rhs]\n", "[------+----------------------------------------------------------------------------+------]\n", "[ s1| 8 0 12 0 1 0 0 0 9/10 0 -1/30| 38]\n", "[ x4| 1 0 1/2 1 0 0 0 0 1/10 0 0| 10]\n", "[ s3| -12/5 0 -31/10 0 0 0 1 0 -9/25 0 1/50| 133/5]\n", "[ x2| 1/10 1 2/5 0 0 0 0 0 -1/100 0 1/300| 33/5]\n", "[ s2| 1 0 3/2 0 0 1 0 0 -1/2 0 0| 2]\n", "[ s4| 2 0 1/2 0 0 0 0 1 3/5 0 -1/30| 2]\n", "[ s6| 2 0 1/2 0 0 0 0 0 9/5 1 -1/10| 2]\n", "[------+----------------------------------------------------------------------------+------]\n", "[ Z| -16/5 0 -24/5 0 0 0 0 0 -9/50 0 -1/150| 166/5]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(7,10)" ] }, { "cell_type": "markdown", "id": "830b3c99", "metadata": {}, "source": [ "La variable de holgura $s_6$ y la fila en la que está la eliminamos del problema (en realidad, la seguiremos viendo, pero no la tendremos en cuenta)." ] }, { "cell_type": "code", "execution_count": 40, "id": "51ff67a2", "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11\\right]$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11\\right]$$" ], "text/plain": [ "[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {\\color{green}{s}}_{8} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 8 & 0 & 12 & 0 & 1 & 0 & 0 & 0 & \\frac{9}{10} & 0 & -\\frac{1}{30} & 0 & 38 \\\\\n", "{x}_{4} & 1 & 0 & \\frac{1}{2} & 1 & 0 & 0 & 0 & 0 & \\frac{1}{10} & 0 & 0 & 0 & 10 \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{12}{5} & 0 & -\\frac{31}{10} & 0 & 0 & 0 & 1 & 0 & -\\frac{9}{25} & 0 & \\frac{1}{50} & 0 & \\frac{133}{5} \\\\\n", "{x}_{2} & \\frac{1}{10} & 1 & \\frac{2}{5} & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{100} & 0 & \\frac{1}{300} & 0 & \\frac{33}{5} \\\\\n", "{\\color{green}{s}}_{2} & 1 & 0 & \\frac{3}{2} & 0 & 0 & 1 & 0 & 0 & -\\frac{1}{2} & 0 & 0 & 0 & 2 \\\\\n", "{\\color{green}{s}}_{4} & 2 & 0 & \\frac{1}{2} & 0 & 0 & 0 & 0 & 1 & \\frac{3}{5} & 0 & -\\frac{1}{30} & 0 & 2 \\\\\n", "{\\color{green}{s}}_{6} & 2 & 0 & \\frac{1}{2} & 0 & 0 & 0 & 0 & 0 & \\frac{9}{5} & 1 & -\\frac{1}{10} & 0 & 2 \\\\\n", "{\\color{green}{s}}_{8} & -60 & 0 & -15 & 0 & 0 & 0 & 0 & 0 & -54 & 0 & -2 & 1 & -60 \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{16}{5} & 0 & -\\frac{24}{5} & 0 & 0 & 0 & 0 & 0 & -\\frac{9}{50} & 0 & -\\frac{1}{150} & 0 & \\frac{166}{5}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {\\color{green}{s}}_{8} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 8 & 0 & 12 & 0 & 1 & 0 & 0 & 0 & \\frac{9}{10} & 0 & -\\frac{1}{30} & 0 & 38 \\\\\n", "{x}_{4} & 1 & 0 & \\frac{1}{2} & 1 & 0 & 0 & 0 & 0 & \\frac{1}{10} & 0 & 0 & 0 & 10 \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{12}{5} & 0 & -\\frac{31}{10} & 0 & 0 & 0 & 1 & 0 & -\\frac{9}{25} & 0 & \\frac{1}{50} & 0 & \\frac{133}{5} \\\\\n", "{x}_{2} & \\frac{1}{10} & 1 & \\frac{2}{5} & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{100} & 0 & \\frac{1}{300} & 0 & \\frac{33}{5} \\\\\n", "{\\color{green}{s}}_{2} & 1 & 0 & \\frac{3}{2} & 0 & 0 & 1 & 0 & 0 & -\\frac{1}{2} & 0 & 0 & 0 & 2 \\\\\n", "{\\color{green}{s}}_{4} & 2 & 0 & \\frac{1}{2} & 0 & 0 & 0 & 0 & 1 & \\frac{3}{5} & 0 & -\\frac{1}{30} & 0 & 2 \\\\\n", "{\\color{green}{s}}_{6} & 2 & 0 & \\frac{1}{2} & 0 & 0 & 0 & 0 & 0 & \\frac{9}{5} & 1 & -\\frac{1}{10} & 0 & 2 \\\\\n", "{\\color{green}{s}}_{8} & -60 & 0 & -15 & 0 & 0 & 0 & 0 & 0 & -54 & 0 & -2 & 1 & -60 \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{16}{5} & 0 & -\\frac{24}{5} & 0 & 0 & 0 & 0 & 0 & -\\frac{9}{50} & 0 & -\\frac{1}{150} & 0 & \\frac{166}{5}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7 s8| rhs]\n", "[------+-----------------------------------------------------------------------------------+------]\n", "[ s1| 8 0 12 0 1 0 0 0 9/10 0 -1/30 0| 38]\n", "[ x4| 1 0 1/2 1 0 0 0 0 1/10 0 0 0| 10]\n", "[ s3| -12/5 0 -31/10 0 0 0 1 0 -9/25 0 1/50 0| 133/5]\n", "[ x2| 1/10 1 2/5 0 0 0 0 0 -1/100 0 1/300 0| 33/5]\n", "[ s2| 1 0 3/2 0 0 1 0 0 -1/2 0 0 0| 2]\n", "[ s4| 2 0 1/2 0 0 0 0 1 3/5 0 -1/30 0| 2]\n", "[ s6| 2 0 1/2 0 0 0 0 0 9/5 1 -1/10 0| 2]\n", "[ s8| -60 0 -15 0 0 0 0 0 -54 0 -2 1| -60]\n", "[------+-----------------------------------------------------------------------------------+------]\n", "[ Z| -16/5 0 -24/5 0 0 0 0 0 -9/50 0 -1/150 0| 166/5]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "corte(3)" ] }, { "cell_type": "code", "execution_count": 41, "id": "0d168d69", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[ 0.053333 NO 0.32000 NO NO NO NO NO 0.0033333 NO 0.0033333 NO]" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cocientesD(8)" ] }, { "cell_type": "code", "execution_count": 42, "id": "c910a995", "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {\\color{green}{s}}_{8} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 9 & 0 & \\frac{49}{4} & 0 & 1 & 0 & 0 & 0 & \\frac{9}{5} & 0 & 0 & -\\frac{1}{60} & 39 \\\\\n", "{x}_{4} & 1 & 0 & \\frac{1}{2} & 1 & 0 & 0 & 0 & 0 & \\frac{1}{10} & 0 & 0 & 0 & 10 \\\\\n", "{\\color{green}{s}}_{3} & -3 & 0 & -\\frac{13}{4} & 0 & 0 & 0 & 1 & 0 & -\\frac{9}{10} & 0 & 0 & \\frac{1}{100} & 26 \\\\\n", "{x}_{2} & 0 & 1 & \\frac{3}{8} & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{10} & 0 & 0 & \\frac{1}{600} & \\frac{13}{2} \\\\\n", "{\\color{green}{s}}_{2} & 1 & 0 & \\frac{3}{2} & 0 & 0 & 1 & 0 & 0 & -\\frac{1}{2} & 0 & 0 & 0 & 2 \\\\\n", "{\\color{green}{s}}_{4} & 3 & 0 & \\frac{3}{4} & 0 & 0 & 0 & 0 & 1 & \\frac{3}{2} & 0 & 0 & -\\frac{1}{60} & 3 \\\\\n", "{\\color{green}{s}}_{6} & 5 & 0 & \\frac{5}{4} & 0 & 0 & 0 & 0 & 0 & \\frac{9}{2} & 1 & 0 & -\\frac{1}{20} & 5 \\\\\n", "{\\color{green}{s}}_{7} & 30 & 0 & \\frac{15}{2} & 0 & 0 & 0 & 0 & 0 & 27 & 0 & 1 & -\\frac{1}{2} & 30 \\\\\n", "\\hline\n", " {Z_{ind}} & -3 & 0 & -\\frac{19}{4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{300} & 33\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {\\color{green}{s}}_{8} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 9 & 0 & \\frac{49}{4} & 0 & 1 & 0 & 0 & 0 & \\frac{9}{5} & 0 & 0 & -\\frac{1}{60} & 39 \\\\\n", "{x}_{4} & 1 & 0 & \\frac{1}{2} & 1 & 0 & 0 & 0 & 0 & \\frac{1}{10} & 0 & 0 & 0 & 10 \\\\\n", "{\\color{green}{s}}_{3} & -3 & 0 & -\\frac{13}{4} & 0 & 0 & 0 & 1 & 0 & -\\frac{9}{10} & 0 & 0 & \\frac{1}{100} & 26 \\\\\n", "{x}_{2} & 0 & 1 & \\frac{3}{8} & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{10} & 0 & 0 & \\frac{1}{600} & \\frac{13}{2} \\\\\n", "{\\color{green}{s}}_{2} & 1 & 0 & \\frac{3}{2} & 0 & 0 & 1 & 0 & 0 & -\\frac{1}{2} & 0 & 0 & 0 & 2 \\\\\n", "{\\color{green}{s}}_{4} & 3 & 0 & \\frac{3}{4} & 0 & 0 & 0 & 0 & 1 & \\frac{3}{2} & 0 & 0 & -\\frac{1}{60} & 3 \\\\\n", "{\\color{green}{s}}_{6} & 5 & 0 & \\frac{5}{4} & 0 & 0 & 0 & 0 & 0 & \\frac{9}{2} & 1 & 0 & -\\frac{1}{20} & 5 \\\\\n", "{\\color{green}{s}}_{7} & 30 & 0 & \\frac{15}{2} & 0 & 0 & 0 & 0 & 0 & 27 & 0 & 1 & -\\frac{1}{2} & 30 \\\\\n", "\\hline\n", " {Z_{ind}} & -3 & 0 & -\\frac{19}{4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{300} & 33\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7 s8| rhs]\n", "[------+-----------------------------------------------------------------------------------+------]\n", "[ s1| 9 0 49/4 0 1 0 0 0 9/5 0 0 -1/60| 39]\n", "[ x4| 1 0 1/2 1 0 0 0 0 1/10 0 0 0| 10]\n", "[ s3| -3 0 -13/4 0 0 0 1 0 -9/10 0 0 1/100| 26]\n", "[ x2| 0 1 3/8 0 0 0 0 0 -1/10 0 0 1/600| 13/2]\n", "[ s2| 1 0 3/2 0 0 1 0 0 -1/2 0 0 0| 2]\n", "[ s4| 3 0 3/4 0 0 0 0 1 3/2 0 0 -1/60| 3]\n", "[ s6| 5 0 5/4 0 0 0 0 0 9/2 1 0 -1/20| 5]\n", "[ s7| 30 0 15/2 0 0 0 0 0 27 0 1 -1/2| 30]\n", "[------+-----------------------------------------------------------------------------------+------]\n", "[ Z| -3 0 -19/4 0 0 0 0 0 0 0 0 -1/300| 33]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(8,11)" ] }, { "cell_type": "markdown", "id": "cea0a25a", "metadata": {}, "source": [ "Las variables de holgura $s_6$ y $s_7$ y las filas en las que están las eliminamos del problema (en realidad, las seguiremos viendo, pero no las tendremos en cuenta)." ] }, { "cell_type": "code", "execution_count": 43, "id": "ab6e7f33", "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\\right]$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\\right]$$" ], "text/plain": [ "[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {\\color{green}{s}}_{8} & {\\color{green}{s}}_{9} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 9 & 0 & \\frac{49}{4} & 0 & 1 & 0 & 0 & 0 & \\frac{9}{5} & 0 & 0 & -\\frac{1}{60} & 0 & 39 \\\\\n", "{x}_{4} & 1 & 0 & \\frac{1}{2} & 1 & 0 & 0 & 0 & 0 & \\frac{1}{10} & 0 & 0 & 0 & 0 & 10 \\\\\n", "{\\color{green}{s}}_{3} & -3 & 0 & -\\frac{13}{4} & 0 & 0 & 0 & 1 & 0 & -\\frac{9}{10} & 0 & 0 & \\frac{1}{100} & 0 & 26 \\\\\n", "{x}_{2} & 0 & 1 & \\frac{3}{8} & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{10} & 0 & 0 & \\frac{1}{600} & 0 & \\frac{13}{2} \\\\\n", "{\\color{green}{s}}_{2} & 1 & 0 & \\frac{3}{2} & 0 & 0 & 1 & 0 & 0 & -\\frac{1}{2} & 0 & 0 & 0 & 0 & 2 \\\\\n", "{\\color{green}{s}}_{4} & 3 & 0 & \\frac{3}{4} & 0 & 0 & 0 & 0 & 1 & \\frac{3}{2} & 0 & 0 & -\\frac{1}{60} & 0 & 3 \\\\\n", "{\\color{green}{s}}_{6} & 5 & 0 & \\frac{5}{4} & 0 & 0 & 0 & 0 & 0 & \\frac{9}{2} & 1 & 0 & -\\frac{1}{20} & 0 & 5 \\\\\n", "{\\color{green}{s}}_{7} & 30 & 0 & \\frac{15}{2} & 0 & 0 & 0 & 0 & 0 & 27 & 0 & 1 & -\\frac{1}{2} & 0 & 30 \\\\\n", "{\\color{green}{s}}_{9} & 0 & 0 & -225 & 0 & 0 & 0 & 0 & 0 & -60 & 0 & 0 & -1 & 1 & -300 \\\\\n", "\\hline\n", " {Z_{ind}} & -3 & 0 & -\\frac{19}{4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{300} & 0 & 33\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {\\color{green}{s}}_{8} & {\\color{green}{s}}_{9} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 9 & 0 & \\frac{49}{4} & 0 & 1 & 0 & 0 & 0 & \\frac{9}{5} & 0 & 0 & -\\frac{1}{60} & 0 & 39 \\\\\n", "{x}_{4} & 1 & 0 & \\frac{1}{2} & 1 & 0 & 0 & 0 & 0 & \\frac{1}{10} & 0 & 0 & 0 & 0 & 10 \\\\\n", "{\\color{green}{s}}_{3} & -3 & 0 & -\\frac{13}{4} & 0 & 0 & 0 & 1 & 0 & -\\frac{9}{10} & 0 & 0 & \\frac{1}{100} & 0 & 26 \\\\\n", "{x}_{2} & 0 & 1 & \\frac{3}{8} & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{10} & 0 & 0 & \\frac{1}{600} & 0 & \\frac{13}{2} \\\\\n", "{\\color{green}{s}}_{2} & 1 & 0 & \\frac{3}{2} & 0 & 0 & 1 & 0 & 0 & -\\frac{1}{2} & 0 & 0 & 0 & 0 & 2 \\\\\n", "{\\color{green}{s}}_{4} & 3 & 0 & \\frac{3}{4} & 0 & 0 & 0 & 0 & 1 & \\frac{3}{2} & 0 & 0 & -\\frac{1}{60} & 0 & 3 \\\\\n", "{\\color{green}{s}}_{6} & 5 & 0 & \\frac{5}{4} & 0 & 0 & 0 & 0 & 0 & \\frac{9}{2} & 1 & 0 & -\\frac{1}{20} & 0 & 5 \\\\\n", "{\\color{green}{s}}_{7} & 30 & 0 & \\frac{15}{2} & 0 & 0 & 0 & 0 & 0 & 27 & 0 & 1 & -\\frac{1}{2} & 0 & 30 \\\\\n", "{\\color{green}{s}}_{9} & 0 & 0 & -225 & 0 & 0 & 0 & 0 & 0 & -60 & 0 & 0 & -1 & 1 & -300 \\\\\n", "\\hline\n", " {Z_{ind}} & -3 & 0 & -\\frac{19}{4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{300} & 0 & 33\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7 s8 s9| rhs]\n", "[------+------------------------------------------------------------------------------------------+------]\n", "[ s1| 9 0 49/4 0 1 0 0 0 9/5 0 0 -1/60 0| 39]\n", "[ x4| 1 0 1/2 1 0 0 0 0 1/10 0 0 0 0| 10]\n", "[ s3| -3 0 -13/4 0 0 0 1 0 -9/10 0 0 1/100 0| 26]\n", "[ x2| 0 1 3/8 0 0 0 0 0 -1/10 0 0 1/600 0| 13/2]\n", "[ s2| 1 0 3/2 0 0 1 0 0 -1/2 0 0 0 0| 2]\n", "[ s4| 3 0 3/4 0 0 0 0 1 3/2 0 0 -1/60 0| 3]\n", "[ s6| 5 0 5/4 0 0 0 0 0 9/2 1 0 -1/20 0| 5]\n", "[ s7| 30 0 15/2 0 0 0 0 0 27 0 1 -1/2 0| 30]\n", "[ s9| 0 0 -225 0 0 0 0 0 -60 0 0 -1 1| -300]\n", "[------+------------------------------------------------------------------------------------------+------]\n", "[ Z| -3 0 -19/4 0 0 0 0 0 0 0 0 -1/300 0| 33]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "corte(4)" ] }, { "cell_type": "code", "execution_count": 44, "id": "8d4e8d64", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[ NO NO 0.021111 NO NO NO NO NO 0.00000 NO NO 0.0033333 NO]" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cocientesD(9)" ] }, { "cell_type": "code", "execution_count": 45, "id": "bf609bbe", "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {\\color{green}{s}}_{8} & {\\color{green}{s}}_{9} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 9 & 0 & \\frac{11}{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -\\frac{7}{150} & \\frac{3}{100} & 30 \\\\\n", "{x}_{4} & 1 & 0 & \\frac{1}{8} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{600} & \\frac{1}{600} & \\frac{19}{2} \\\\\n", "{\\color{green}{s}}_{3} & -3 & 0 & \\frac{1}{8} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & \\frac{1}{40} & -\\frac{3}{200} & \\frac{61}{2} \\\\\n", "{x}_{2} & 0 & 1 & \\frac{3}{4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \\frac{1}{300} & -\\frac{1}{600} & 7 \\\\\n", "{\\color{green}{s}}_{2} & 1 & 0 & \\frac{27}{8} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & \\frac{1}{120} & -\\frac{1}{120} & \\frac{9}{2} \\\\\n", "{\\color{green}{s}}_{4} & 3 & 0 & -\\frac{39}{8} & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & -\\frac{1}{24} & \\frac{1}{40} & -\\frac{9}{2} \\\\\n", "{\\color{green}{s}}_{6} & 5 & 0 & -\\frac{125}{8} & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & -\\frac{1}{8} & \\frac{3}{40} & -\\frac{35}{2} \\\\\n", "{\\color{green}{s}}_{7} & 30 & 0 & -\\frac{375}{4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -\\frac{19}{20} & \\frac{9}{20} & -105 \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & \\frac{15}{4} & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & \\frac{1}{60} & -\\frac{1}{60} & 5 \\\\\n", "\\hline\n", " {Z_{ind}} & -3 & 0 & -\\frac{19}{4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{300} & 0 & 33\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {\\color{green}{s}}_{8} & {\\color{green}{s}}_{9} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 9 & 0 & \\frac{11}{2} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -\\frac{7}{150} & \\frac{3}{100} & 30 \\\\\n", "{x}_{4} & 1 & 0 & \\frac{1}{8} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{600} & \\frac{1}{600} & \\frac{19}{2} \\\\\n", "{\\color{green}{s}}_{3} & -3 & 0 & \\frac{1}{8} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & \\frac{1}{40} & -\\frac{3}{200} & \\frac{61}{2} \\\\\n", "{x}_{2} & 0 & 1 & \\frac{3}{4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \\frac{1}{300} & -\\frac{1}{600} & 7 \\\\\n", "{\\color{green}{s}}_{2} & 1 & 0 & \\frac{27}{8} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & \\frac{1}{120} & -\\frac{1}{120} & \\frac{9}{2} \\\\\n", "{\\color{green}{s}}_{4} & 3 & 0 & -\\frac{39}{8} & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & -\\frac{1}{24} & \\frac{1}{40} & -\\frac{9}{2} \\\\\n", "{\\color{green}{s}}_{6} & 5 & 0 & -\\frac{125}{8} & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & -\\frac{1}{8} & \\frac{3}{40} & -\\frac{35}{2} \\\\\n", "{\\color{green}{s}}_{7} & 30 & 0 & -\\frac{375}{4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -\\frac{19}{20} & \\frac{9}{20} & -105 \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & \\frac{15}{4} & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & \\frac{1}{60} & -\\frac{1}{60} & 5 \\\\\n", "\\hline\n", " {Z_{ind}} & -3 & 0 & -\\frac{19}{4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{300} & 0 & 33\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7 s8 s9| rhs]\n", "[------+------------------------------------------------------------------------------------------+------]\n", "[ s1| 9 0 11/2 0 1 0 0 0 0 0 0 -7/150 3/100| 30]\n", "[ x4| 1 0 1/8 1 0 0 0 0 0 0 0 -1/600 1/600| 19/2]\n", "[ s3| -3 0 1/8 0 0 0 1 0 0 0 0 1/40 -3/200| 61/2]\n", "[ x2| 0 1 3/4 0 0 0 0 0 0 0 0 1/300 -1/600| 7]\n", "[ s2| 1 0 27/8 0 0 1 0 0 0 0 0 1/120 -1/120| 9/2]\n", "[ s4| 3 0 -39/8 0 0 0 0 1 0 0 0 -1/24 1/40| -9/2]\n", "[ s6| 5 0 -125/8 0 0 0 0 0 0 1 0 -1/8 3/40| -35/2]\n", "[ s7| 30 0 -375/4 0 0 0 0 0 0 0 1 -19/20 9/20| -105]\n", "[ s5| 0 0 15/4 0 0 0 0 0 1 0 0 1/60 -1/60| 5]\n", "[------+------------------------------------------------------------------------------------------+------]\n", "[ Z| -3 0 -19/4 0 0 0 0 0 0 0 0 -1/300 0| 33]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(9,9)" ] }, { "cell_type": "code", "execution_count": 46, "id": "d39e5848", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[ NO NO 0.97436 NO NO NO NO NO NO NO NO 0.080000 NO]" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cocientesD(6)" ] }, { "cell_type": "code", "execution_count": 47, "id": "667a82db", "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {\\color{green}{s}}_{8} & {\\color{green}{s}}_{9} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & \\frac{141}{25} & 0 & \\frac{274}{25} & 0 & 1 & 0 & 0 & -\\frac{28}{25} & 0 & 0 & 0 & 0 & \\frac{1}{500} & \\frac{876}{25} \\\\\n", "{x}_{4} & \\frac{22}{25} & 0 & \\frac{8}{25} & 1 & 0 & 0 & 0 & -\\frac{1}{25} & 0 & 0 & 0 & 0 & \\frac{1}{1500} & \\frac{242}{25} \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{6}{5} & 0 & -\\frac{14}{5} & 0 & 0 & 0 & 1 & \\frac{3}{5} & 0 & 0 & 0 & 0 & 0 & \\frac{139}{5} \\\\\n", "{x}_{2} & \\frac{6}{25} & 1 & \\frac{9}{25} & 0 & 0 & 0 & 0 & \\frac{2}{25} & 0 & 0 & 0 & 0 & \\frac{1}{3000} & \\frac{166}{25} \\\\\n", "{\\color{green}{s}}_{2} & \\frac{8}{5} & 0 & \\frac{12}{5} & 0 & 0 & 1 & 0 & \\frac{1}{5} & 0 & 0 & 0 & 0 & -\\frac{1}{300} & \\frac{18}{5} \\\\\n", "{\\color{green}{s}}_{8} & -72 & 0 & 117 & 0 & 0 & 0 & 0 & -24 & 0 & 0 & 0 & 1 & -\\frac{3}{5} & 108 \\\\\n", "{\\color{green}{s}}_{6} & -4 & 0 & -1 & 0 & 0 & 0 & 0 & -3 & 0 & 1 & 0 & 0 & 0 & -4 \\\\\n", "{\\color{green}{s}}_{7} & -\\frac{192}{5} & 0 & \\frac{87}{5} & 0 & 0 & 0 & 0 & -\\frac{114}{5} & 0 & 0 & 1 & 0 & -\\frac{3}{25} & -\\frac{12}{5} \\\\\n", "{\\color{green}{s}}_{5} & \\frac{6}{5} & 0 & \\frac{9}{5} & 0 & 0 & 0 & 0 & \\frac{2}{5} & 1 & 0 & 0 & 0 & -\\frac{1}{150} & \\frac{16}{5} \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{81}{25} & 0 & -\\frac{109}{25} & 0 & 0 & 0 & 0 & -\\frac{2}{25} & 0 & 0 & 0 & 0 & -\\frac{1}{500} & \\frac{816}{25}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {\\color{green}{s}}_{8} & {\\color{green}{s}}_{9} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & \\frac{141}{25} & 0 & \\frac{274}{25} & 0 & 1 & 0 & 0 & -\\frac{28}{25} & 0 & 0 & 0 & 0 & \\frac{1}{500} & \\frac{876}{25} \\\\\n", "{x}_{4} & \\frac{22}{25} & 0 & \\frac{8}{25} & 1 & 0 & 0 & 0 & -\\frac{1}{25} & 0 & 0 & 0 & 0 & \\frac{1}{1500} & \\frac{242}{25} \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{6}{5} & 0 & -\\frac{14}{5} & 0 & 0 & 0 & 1 & \\frac{3}{5} & 0 & 0 & 0 & 0 & 0 & \\frac{139}{5} \\\\\n", "{x}_{2} & \\frac{6}{25} & 1 & \\frac{9}{25} & 0 & 0 & 0 & 0 & \\frac{2}{25} & 0 & 0 & 0 & 0 & \\frac{1}{3000} & \\frac{166}{25} \\\\\n", "{\\color{green}{s}}_{2} & \\frac{8}{5} & 0 & \\frac{12}{5} & 0 & 0 & 1 & 0 & \\frac{1}{5} & 0 & 0 & 0 & 0 & -\\frac{1}{300} & \\frac{18}{5} \\\\\n", "{\\color{green}{s}}_{8} & -72 & 0 & 117 & 0 & 0 & 0 & 0 & -24 & 0 & 0 & 0 & 1 & -\\frac{3}{5} & 108 \\\\\n", "{\\color{green}{s}}_{6} & -4 & 0 & -1 & 0 & 0 & 0 & 0 & -3 & 0 & 1 & 0 & 0 & 0 & -4 \\\\\n", "{\\color{green}{s}}_{7} & -\\frac{192}{5} & 0 & \\frac{87}{5} & 0 & 0 & 0 & 0 & -\\frac{114}{5} & 0 & 0 & 1 & 0 & -\\frac{3}{25} & -\\frac{12}{5} \\\\\n", "{\\color{green}{s}}_{5} & \\frac{6}{5} & 0 & \\frac{9}{5} & 0 & 0 & 0 & 0 & \\frac{2}{5} & 1 & 0 & 0 & 0 & -\\frac{1}{150} & \\frac{16}{5} \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{81}{25} & 0 & -\\frac{109}{25} & 0 & 0 & 0 & 0 & -\\frac{2}{25} & 0 & 0 & 0 & 0 & -\\frac{1}{500} & \\frac{816}{25}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7 s8 s9| rhs]\n", "[-------+-------------------------------------------------------------------------------------------------------+-------]\n", "[ s1| 141/25 0 274/25 0 1 0 0 -28/25 0 0 0 0 1/500| 876/25]\n", "[ x4| 22/25 0 8/25 1 0 0 0 -1/25 0 0 0 0 1/1500| 242/25]\n", "[ s3| -6/5 0 -14/5 0 0 0 1 3/5 0 0 0 0 0| 139/5]\n", "[ x2| 6/25 1 9/25 0 0 0 0 2/25 0 0 0 0 1/3000| 166/25]\n", "[ s2| 8/5 0 12/5 0 0 1 0 1/5 0 0 0 0 -1/300| 18/5]\n", "[ s8| -72 0 117 0 0 0 0 -24 0 0 0 1 -3/5| 108]\n", "[ s6| -4 0 -1 0 0 0 0 -3 0 1 0 0 0| -4]\n", "[ s7| -192/5 0 87/5 0 0 0 0 -114/5 0 0 1 0 -3/25| -12/5]\n", "[ s5| 6/5 0 9/5 0 0 0 0 2/5 1 0 0 0 -1/150| 16/5]\n", "[-------+-------------------------------------------------------------------------------------------------------+-------]\n", "[ Z| -81/25 0 -109/25 0 0 0 0 -2/25 0 0 0 0 -1/500| 816/25]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(6,12)" ] }, { "cell_type": "markdown", "id": "3031c651", "metadata": {}, "source": [ "Las variables de holgura $s_5,$ $s_6, $ $s_7$ y $s_8$ y las filas en las que están las eliminamos del problema (en realidad, las seguiremos viendo, pero no las tendremos en cuenta)." ] }, { "cell_type": "code", "execution_count": 48, "id": "284b88c7", "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13\\right]$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13\\right]$$" ], "text/plain": [ "[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {\\color{green}{s}}_{8} & {\\color{green}{s}}_{9} & {\\color{green}{s}}_{10} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & \\frac{141}{25} & 0 & \\frac{274}{25} & 0 & 1 & 0 & 0 & -\\frac{28}{25} & 0 & 0 & 0 & 0 & \\frac{1}{500} & 0 & \\frac{876}{25} \\\\\n", "{x}_{4} & \\frac{22}{25} & 0 & \\frac{8}{25} & 1 & 0 & 0 & 0 & -\\frac{1}{25} & 0 & 0 & 0 & 0 & \\frac{1}{1500} & 0 & \\frac{242}{25} \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{6}{5} & 0 & -\\frac{14}{5} & 0 & 0 & 0 & 1 & \\frac{3}{5} & 0 & 0 & 0 & 0 & 0 & 0 & \\frac{139}{5} \\\\\n", "{x}_{2} & \\frac{6}{25} & 1 & \\frac{9}{25} & 0 & 0 & 0 & 0 & \\frac{2}{25} & 0 & 0 & 0 & 0 & \\frac{1}{3000} & 0 & \\frac{166}{25} \\\\\n", "{\\color{green}{s}}_{2} & \\frac{8}{5} & 0 & \\frac{12}{5} & 0 & 0 & 1 & 0 & \\frac{1}{5} & 0 & 0 & 0 & 0 & -\\frac{1}{300} & 0 & \\frac{18}{5} \\\\\n", "{\\color{green}{s}}_{8} & -72 & 0 & 117 & 0 & 0 & 0 & 0 & -24 & 0 & 0 & 0 & 1 & -\\frac{3}{5} & 0 & 108 \\\\\n", "{\\color{green}{s}}_{6} & -4 & 0 & -1 & 0 & 0 & 0 & 0 & -3 & 0 & 1 & 0 & 0 & 0 & 0 & -4 \\\\\n", "{\\color{green}{s}}_{7} & -\\frac{192}{5} & 0 & \\frac{87}{5} & 0 & 0 & 0 & 0 & -\\frac{114}{5} & 0 & 0 & 1 & 0 & -\\frac{3}{25} & 0 & -\\frac{12}{5} \\\\\n", "{\\color{green}{s}}_{5} & \\frac{6}{5} & 0 & \\frac{9}{5} & 0 & 0 & 0 & 0 & \\frac{2}{5} & 1 & 0 & 0 & 0 & -\\frac{1}{150} & 0 & \\frac{16}{5} \\\\\n", "{\\color{green}{s}}_{10} & -45 & 0 & -5 & 0 & 0 & 0 & 0 & -15 & 0 & 0 & 0 & 0 & -6 & 1 & -120 \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{81}{25} & 0 & -\\frac{109}{25} & 0 & 0 & 0 & 0 & -\\frac{2}{25} & 0 & 0 & 0 & 0 & -\\frac{1}{500} & 0 & \\frac{816}{25}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrrr|r}\n", "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {\\color{green}{s}}_{4} & {\\color{green}{s}}_{5} & {\\color{green}{s}}_{6} & {\\color{green}{s}}_{7} & {\\color{green}{s}}_{8} & {\\color{green}{s}}_{9} & {\\color{green}{s}}_{10} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & \\frac{141}{25} & 0 & \\frac{274}{25} & 0 & 1 & 0 & 0 & -\\frac{28}{25} & 0 & 0 & 0 & 0 & \\frac{1}{500} & 0 & \\frac{876}{25} \\\\\n", "{x}_{4} & \\frac{22}{25} & 0 & \\frac{8}{25} & 1 & 0 & 0 & 0 & -\\frac{1}{25} & 0 & 0 & 0 & 0 & \\frac{1}{1500} & 0 & \\frac{242}{25} \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{6}{5} & 0 & -\\frac{14}{5} & 0 & 0 & 0 & 1 & \\frac{3}{5} & 0 & 0 & 0 & 0 & 0 & 0 & \\frac{139}{5} \\\\\n", "{x}_{2} & \\frac{6}{25} & 1 & \\frac{9}{25} & 0 & 0 & 0 & 0 & \\frac{2}{25} & 0 & 0 & 0 & 0 & \\frac{1}{3000} & 0 & \\frac{166}{25} \\\\\n", "{\\color{green}{s}}_{2} & \\frac{8}{5} & 0 & \\frac{12}{5} & 0 & 0 & 1 & 0 & \\frac{1}{5} & 0 & 0 & 0 & 0 & -\\frac{1}{300} & 0 & \\frac{18}{5} \\\\\n", "{\\color{green}{s}}_{8} & -72 & 0 & 117 & 0 & 0 & 0 & 0 & -24 & 0 & 0 & 0 & 1 & -\\frac{3}{5} & 0 & 108 \\\\\n", "{\\color{green}{s}}_{6} & -4 & 0 & -1 & 0 & 0 & 0 & 0 & -3 & 0 & 1 & 0 & 0 & 0 & 0 & -4 \\\\\n", "{\\color{green}{s}}_{7} & -\\frac{192}{5} & 0 & \\frac{87}{5} & 0 & 0 & 0 & 0 & -\\frac{114}{5} & 0 & 0 & 1 & 0 & -\\frac{3}{25} & 0 & -\\frac{12}{5} \\\\\n", "{\\color{green}{s}}_{5} & \\frac{6}{5} & 0 & \\frac{9}{5} & 0 & 0 & 0 & 0 & \\frac{2}{5} & 1 & 0 & 0 & 0 & -\\frac{1}{150} & 0 & \\frac{16}{5} \\\\\n", "{\\color{green}{s}}_{10} & -45 & 0 & -5 & 0 & 0 & 0 & 0 & -15 & 0 & 0 & 0 & 0 & -6 & 1 & -120 \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{81}{25} & 0 & -\\frac{109}{25} & 0 & 0 & 0 & 0 & -\\frac{2}{25} & 0 & 0 & 0 & 0 & -\\frac{1}{500} & 0 & \\frac{816}{25}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7 s8 s9 s10| rhs]\n", "[-------+---------------------------------------------------------------------------------------------------------------+-------]\n", "[ s1| 141/25 0 274/25 0 1 0 0 -28/25 0 0 0 0 1/500 0| 876/25]\n", "[ x4| 22/25 0 8/25 1 0 0 0 -1/25 0 0 0 0 1/1500 0| 242/25]\n", "[ s3| -6/5 0 -14/5 0 0 0 1 3/5 0 0 0 0 0 0| 139/5]\n", "[ x2| 6/25 1 9/25 0 0 0 0 2/25 0 0 0 0 1/3000 0| 166/25]\n", "[ s2| 8/5 0 12/5 0 0 1 0 1/5 0 0 0 0 -1/300 0| 18/5]\n", "[ s8| -72 0 117 0 0 0 0 -24 0 0 0 1 -3/5 0| 108]\n", "[ s6| -4 0 -1 0 0 0 0 -3 0 1 0 0 0 0| -4]\n", "[ s7| -192/5 0 87/5 0 0 0 0 -114/5 0 0 1 0 -3/25 0| -12/5]\n", "[ s5| 6/5 0 9/5 0 0 0 0 2/5 1 0 0 0 -1/150 0| 16/5]\n", "[ s10| -45 0 -5 0 0 0 0 -15 0 0 0 0 -6 1| -120]\n", "[-------+---------------------------------------------------------------------------------------------------------------+-------]\n", "[ Z| -81/25 0 -109/25 0 0 0 0 -2/25 0 0 0 0 -1/500 0| 816/25]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "corte(1)" ] }, { "cell_type": "code", "execution_count": 49, "id": "2b15052d", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[ 0.072000 NO 0.87200 NO NO NO NO 0.0053333 NO NO NO NO 0.00033333 NO]" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cocientesD(10)" ] }, { "cell_type": "code", "execution_count": 50, "id": "aaea9aa1", "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrrr|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} & {\\color{green}{s}}_{8} & {\\color{green}{s}}_{9} & {\\color{green}{s}}_{10} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & \\frac{45}{8} & 0 & \\frac{263}{24} & 0 & 1 & 0 & 0 & -\\frac{9}{8} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{3000} & 35 \\\\\n", "{x}_{4} & \\frac{7}{8} & 0 & \\frac{23}{72} & 1 & 0 & 0 & 0 & -\\frac{1}{24} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{9000} & \\frac{29}{3} \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{6}{5} & 0 & -\\frac{14}{5} & 0 & 0 & 0 & 1 & \\frac{3}{5} & 0 & 0 & 0 & 0 & 0 & 0 & \\frac{139}{5} \\\\\n", "{x}_{2} & \\frac{19}{80} & 1 & \\frac{259}{720} & 0 & 0 & 0 & 0 & \\frac{19}{240} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{18000} & \\frac{199}{30} \\\\\n", "{\\color{green}{s}}_{2} & \\frac{13}{8} & 0 & \\frac{173}{72} & 0 & 0 & 1 & 0 & \\frac{5}{24} & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{1800} & \\frac{11}{3} \\\\\n", "{\\color{green}{s}}_{8} & -\\frac{135}{2} & 0 & \\frac{235}{2} & 0 & 0 & 0 & 0 & -\\frac{45}{2} & 0 & 0 & 0 & 1 & 0 & -\\frac{1}{10} & 120 \\\\\n", "{\\color{green}{s}}_{6} & -4 & 0 & -1 & 0 & 0 & 0 & 0 & -3 & 0 & 1 & 0 & 0 & 0 & 0 & -4 \\\\\n", "{\\color{green}{s}}_{7} & -\\frac{75}{2} & 0 & \\frac{35}{2} & 0 & 0 & 0 & 0 & -\\frac{45}{2} & 0 & 0 & 1 & 0 & 0 & -\\frac{1}{50} & 0 \\\\\n", "{\\color{green}{s}}_{5} & \\frac{5}{4} & 0 & \\frac{65}{36} & 0 & 0 & 0 & 0 & \\frac{5}{12} & 1 & 0 & 0 & 0 & 0 & -\\frac{1}{900} & \\frac{10}{3} \\\\\n", "{\\color{green}{s}}_{9} & \\frac{15}{2} & 0 & \\frac{5}{6} & 0 & 0 & 0 & 0 & \\frac{5}{2} & 0 & 0 & 0 & 0 & 1 & -\\frac{1}{6} & 20 \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{129}{40} & 0 & -\\frac{523}{120} & 0 & 0 & 0 & 0 & -\\frac{3}{40} & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{3000} & \\frac{163}{5}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrrr|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} & {\\color{green}{s}}_{8} & {\\color{green}{s}}_{9} & {\\color{green}{s}}_{10} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & \\frac{45}{8} & 0 & \\frac{263}{24} & 0 & 1 & 0 & 0 & -\\frac{9}{8} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{3000} & 35 \\\\\n", "{x}_{4} & \\frac{7}{8} & 0 & \\frac{23}{72} & 1 & 0 & 0 & 0 & -\\frac{1}{24} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{9000} & \\frac{29}{3} \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{6}{5} & 0 & -\\frac{14}{5} & 0 & 0 & 0 & 1 & \\frac{3}{5} & 0 & 0 & 0 & 0 & 0 & 0 & \\frac{139}{5} \\\\\n", "{x}_{2} & \\frac{19}{80} & 1 & \\frac{259}{720} & 0 & 0 & 0 & 0 & \\frac{19}{240} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{18000} & \\frac{199}{30} \\\\\n", "{\\color{green}{s}}_{2} & \\frac{13}{8} & 0 & \\frac{173}{72} & 0 & 0 & 1 & 0 & \\frac{5}{24} & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{1800} & \\frac{11}{3} \\\\\n", "{\\color{green}{s}}_{8} & -\\frac{135}{2} & 0 & \\frac{235}{2} & 0 & 0 & 0 & 0 & -\\frac{45}{2} & 0 & 0 & 0 & 1 & 0 & -\\frac{1}{10} & 120 \\\\\n", "{\\color{green}{s}}_{6} & -4 & 0 & -1 & 0 & 0 & 0 & 0 & -3 & 0 & 1 & 0 & 0 & 0 & 0 & -4 \\\\\n", "{\\color{green}{s}}_{7} & -\\frac{75}{2} & 0 & \\frac{35}{2} & 0 & 0 & 0 & 0 & -\\frac{45}{2} & 0 & 0 & 1 & 0 & 0 & -\\frac{1}{50} & 0 \\\\\n", "{\\color{green}{s}}_{5} & \\frac{5}{4} & 0 & \\frac{65}{36} & 0 & 0 & 0 & 0 & \\frac{5}{12} & 1 & 0 & 0 & 0 & 0 & -\\frac{1}{900} & \\frac{10}{3} \\\\\n", "{\\color{green}{s}}_{9} & \\frac{15}{2} & 0 & \\frac{5}{6} & 0 & 0 & 0 & 0 & \\frac{5}{2} & 0 & 0 & 0 & 0 & 1 & -\\frac{1}{6} & 20 \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{129}{40} & 0 & -\\frac{523}{120} & 0 & 0 & 0 & 0 & -\\frac{3}{40} & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{3000} & \\frac{163}{5}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7 s8 s9 s10| rhs]\n", "[--------+-----------------------------------------------------------------------------------------------------------------------------+--------]\n", "[ s1| 45/8 0 263/24 0 1 0 0 -9/8 0 0 0 0 0 1/3000| 35]\n", "[ x4| 7/8 0 23/72 1 0 0 0 -1/24 0 0 0 0 0 1/9000| 29/3]\n", "[ s3| -6/5 0 -14/5 0 0 0 1 3/5 0 0 0 0 0 0| 139/5]\n", "[ x2| 19/80 1 259/720 0 0 0 0 19/240 0 0 0 0 0 1/18000| 199/30]\n", "[ s2| 13/8 0 173/72 0 0 1 0 5/24 0 0 0 0 0 -1/1800| 11/3]\n", "[ s8| -135/2 0 235/2 0 0 0 0 -45/2 0 0 0 1 0 -1/10| 120]\n", "[ s6| -4 0 -1 0 0 0 0 -3 0 1 0 0 0 0| -4]\n", "[ s7| -75/2 0 35/2 0 0 0 0 -45/2 0 0 1 0 0 -1/50| 0]\n", "[ s5| 5/4 0 65/36 0 0 0 0 5/12 1 0 0 0 0 -1/900| 10/3]\n", "[ s9| 15/2 0 5/6 0 0 0 0 5/2 0 0 0 0 1 -1/6| 20]\n", "[--------+-----------------------------------------------------------------------------------------------------------------------------+--------]\n", "[ Z| -129/40 0 -523/120 0 0 0 0 -3/40 0 0 0 0 0 -1/3000| 163/5]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(10,13)" ] }, { "cell_type": "markdown", "id": "5fa4bd30", "metadata": {}, "source": [ "Las variables de holgura $s_5,$ $s_6, $ $s_7$ $s_8$ y $s_9$ y las filas en las que están las eliminamos del problema (en realidad, las seguiremos viendo, pero no las tendremos en cuenta)." ] }, { "cell_type": "code", "execution_count": 51, "id": "d65c5d72", "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14\\right]$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14\\right]$$" ], "text/plain": [ "[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrrrr|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} & {\\color{green}{s}}_{8} & {\\color{green}{s}}_{9} & {\\color{green}{s}}_{10} & {\\color{green}{s}}_{11} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & \\frac{45}{8} & 0 & \\frac{263}{24} & 0 & 1 & 0 & 0 & -\\frac{9}{8} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{3000} & 0 & 35 \\\\\n", "{x}_{4} & \\frac{7}{8} & 0 & \\frac{23}{72} & 1 & 0 & 0 & 0 & -\\frac{1}{24} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{9000} & 0 & \\frac{29}{3} \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{6}{5} & 0 & -\\frac{14}{5} & 0 & 0 & 0 & 1 & \\frac{3}{5} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \\frac{139}{5} \\\\\n", "{x}_{2} & \\frac{19}{80} & 1 & \\frac{259}{720} & 0 & 0 & 0 & 0 & \\frac{19}{240} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{18000} & 0 & \\frac{199}{30} \\\\\n", "{\\color{green}{s}}_{2} & \\frac{13}{8} & 0 & \\frac{173}{72} & 0 & 0 & 1 & 0 & \\frac{5}{24} & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{1800} & 0 & \\frac{11}{3} \\\\\n", "{\\color{green}{s}}_{8} & -\\frac{135}{2} & 0 & \\frac{235}{2} & 0 & 0 & 0 & 0 & -\\frac{45}{2} & 0 & 0 & 0 & 1 & 0 & -\\frac{1}{10} & 0 & 120 \\\\\n", "{\\color{green}{s}}_{6} & -4 & 0 & -1 & 0 & 0 & 0 & 0 & -3 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -4 \\\\\n", "{\\color{green}{s}}_{7} & -\\frac{75}{2} & 0 & \\frac{35}{2} & 0 & 0 & 0 & 0 & -\\frac{45}{2} & 0 & 0 & 1 & 0 & 0 & -\\frac{1}{50} & 0 & 0 \\\\\n", "{\\color{green}{s}}_{5} & \\frac{5}{4} & 0 & \\frac{65}{36} & 0 & 0 & 0 & 0 & \\frac{5}{12} & 1 & 0 & 0 & 0 & 0 & -\\frac{1}{900} & 0 & \\frac{10}{3} \\\\\n", "{\\color{green}{s}}_{9} & \\frac{15}{2} & 0 & \\frac{5}{6} & 0 & 0 & 0 & 0 & \\frac{5}{2} & 0 & 0 & 0 & 0 & 1 & -\\frac{1}{6} & 0 & 20 \\\\\n", "{\\color{green}{s}}_{11} & -2250 & 0 & -2875 & 0 & 0 & 0 & 0 & -750 & 0 & 0 & 0 & 0 & 0 & -1 & 1 & -6000 \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{129}{40} & 0 & -\\frac{523}{120} & 0 & 0 & 0 & 0 & -\\frac{3}{40} & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{3000} & 0 & \\frac{163}{5}\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrrrr|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} & {\\color{green}{s}}_{8} & {\\color{green}{s}}_{9} & {\\color{green}{s}}_{10} & {\\color{green}{s}}_{11} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & \\frac{45}{8} & 0 & \\frac{263}{24} & 0 & 1 & 0 & 0 & -\\frac{9}{8} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{3000} & 0 & 35 \\\\\n", "{x}_{4} & \\frac{7}{8} & 0 & \\frac{23}{72} & 1 & 0 & 0 & 0 & -\\frac{1}{24} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{9000} & 0 & \\frac{29}{3} \\\\\n", "{\\color{green}{s}}_{3} & -\\frac{6}{5} & 0 & -\\frac{14}{5} & 0 & 0 & 0 & 1 & \\frac{3}{5} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \\frac{139}{5} \\\\\n", "{x}_{2} & \\frac{19}{80} & 1 & \\frac{259}{720} & 0 & 0 & 0 & 0 & \\frac{19}{240} & 0 & 0 & 0 & 0 & 0 & \\frac{1}{18000} & 0 & \\frac{199}{30} \\\\\n", "{\\color{green}{s}}_{2} & \\frac{13}{8} & 0 & \\frac{173}{72} & 0 & 0 & 1 & 0 & \\frac{5}{24} & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{1800} & 0 & \\frac{11}{3} \\\\\n", "{\\color{green}{s}}_{8} & -\\frac{135}{2} & 0 & \\frac{235}{2} & 0 & 0 & 0 & 0 & -\\frac{45}{2} & 0 & 0 & 0 & 1 & 0 & -\\frac{1}{10} & 0 & 120 \\\\\n", "{\\color{green}{s}}_{6} & -4 & 0 & -1 & 0 & 0 & 0 & 0 & -3 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & -4 \\\\\n", "{\\color{green}{s}}_{7} & -\\frac{75}{2} & 0 & \\frac{35}{2} & 0 & 0 & 0 & 0 & -\\frac{45}{2} & 0 & 0 & 1 & 0 & 0 & -\\frac{1}{50} & 0 & 0 \\\\\n", "{\\color{green}{s}}_{5} & \\frac{5}{4} & 0 & \\frac{65}{36} & 0 & 0 & 0 & 0 & \\frac{5}{12} & 1 & 0 & 0 & 0 & 0 & -\\frac{1}{900} & 0 & \\frac{10}{3} \\\\\n", "{\\color{green}{s}}_{9} & \\frac{15}{2} & 0 & \\frac{5}{6} & 0 & 0 & 0 & 0 & \\frac{5}{2} & 0 & 0 & 0 & 0 & 1 & -\\frac{1}{6} & 0 & 20 \\\\\n", "{\\color{green}{s}}_{11} & -2250 & 0 & -2875 & 0 & 0 & 0 & 0 & -750 & 0 & 0 & 0 & 0 & 0 & -1 & 1 & -6000 \\\\\n", "\\hline\n", " {Z_{ind}} & -\\frac{129}{40} & 0 & -\\frac{523}{120} & 0 & 0 & 0 & 0 & -\\frac{3}{40} & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{3000} & 0 & \\frac{163}{5}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7 s8 s9 s10 s11| rhs]\n", "[--------+--------------------------------------------------------------------------------------------------------------------------------------+--------]\n", "[ s1| 45/8 0 263/24 0 1 0 0 -9/8 0 0 0 0 0 1/3000 0| 35]\n", "[ x4| 7/8 0 23/72 1 0 0 0 -1/24 0 0 0 0 0 1/9000 0| 29/3]\n", "[ s3| -6/5 0 -14/5 0 0 0 1 3/5 0 0 0 0 0 0 0| 139/5]\n", "[ x2| 19/80 1 259/720 0 0 0 0 19/240 0 0 0 0 0 1/18000 0| 199/30]\n", "[ s2| 13/8 0 173/72 0 0 1 0 5/24 0 0 0 0 0 -1/1800 0| 11/3]\n", "[ s8| -135/2 0 235/2 0 0 0 0 -45/2 0 0 0 1 0 -1/10 0| 120]\n", "[ s6| -4 0 -1 0 0 0 0 -3 0 1 0 0 0 0 0| -4]\n", "[ s7| -75/2 0 35/2 0 0 0 0 -45/2 0 0 1 0 0 -1/50 0| 0]\n", "[ s5| 5/4 0 65/36 0 0 0 0 5/12 1 0 0 0 0 -1/900 0| 10/3]\n", "[ s9| 15/2 0 5/6 0 0 0 0 5/2 0 0 0 0 1 -1/6 0| 20]\n", "[ s11| -2250 0 -2875 0 0 0 0 -750 0 0 0 0 0 -1 1| -6000]\n", "[--------+--------------------------------------------------------------------------------------------------------------------------------------+--------]\n", "[ Z| -129/40 0 -523/120 0 0 0 0 -3/40 0 0 0 0 0 -1/3000 0| 163/5]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "corte(2)" ] }, { "cell_type": "code", "execution_count": 52, "id": "fc8cc78d", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[ 0.0014333 NO 0.0015159 NO NO NO NO 0.00010000 NO NO NO NO NO 0.00033333 NO]" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cocientesD(11)" ] }, { "cell_type": "code", "execution_count": 53, "id": "3f764aec", "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrrrr|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} & {\\color{green}{s}}_{8} & {\\color{green}{s}}_{9} & {\\color{green}{s}}_{10} & {\\color{green}{s}}_{11} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 9 & 0 & \\frac{733}{48} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \\frac{11}{6000} & -\\frac{3}{2000} & 44 \\\\\n", "{x}_{4} & 1 & 0 & \\frac{23}{48} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \\frac{1}{6000} & -\\frac{1}{18000} & 10 \\\\\n", "{\\color{green}{s}}_{3} & -3 & 0 & -\\frac{51}{10} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{1250} & \\frac{1}{1250} & 23 \\\\\n", "{x}_{2} & 0 & 1 & \\frac{9}{160} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{20000} & \\frac{19}{180000} & 6 \\\\\n", "{\\color{green}{s}}_{2} & 1 & 0 & \\frac{77}{48} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{1200} & \\frac{1}{3600} & 2 \\\\\n", "{\\color{green}{s}}_{8} & 0 & 0 & \\frac{815}{4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & -\\frac{7}{100} & -\\frac{3}{100} & 300 \\\\\n", "{\\color{green}{s}}_{6} & 5 & 0 & \\frac{21}{2} & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & \\frac{1}{250} & -\\frac{1}{250} & 20 \\\\\n", "{\\color{green}{s}}_{7} & 30 & 0 & \\frac{415}{4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & \\frac{1}{100} & -\\frac{3}{100} & 180 \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & \\frac{5}{24} & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & -\\frac{1}{600} & \\frac{1}{1800} & 0 \\\\\n", "{\\color{green}{s}}_{9} & 0 & 0 & -\\frac{35}{4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -\\frac{17}{100} & \\frac{1}{300} & 0 \\\\\n", "{\\color{green}{s}}_{4} & 3 & 0 & \\frac{23}{6} & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & \\frac{1}{750} & -\\frac{1}{750} & 8 \\\\\n", "\\hline\n", " {Z_{ind}} & -3 & 0 & -\\frac{977}{240} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -\\frac{7}{30000} & -\\frac{1}{10000} & 32\n", "\\end{array}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r|rrrrrrrrrrrrrrr|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} & {\\color{green}{s}}_{8} & {\\color{green}{s}}_{9} & {\\color{green}{s}}_{10} & {\\color{green}{s}}_{11} & {b} \\\\\n", "\\hline\n", " {\\color{green}{s}}_{1} & 9 & 0 & \\frac{733}{48} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \\frac{11}{6000} & -\\frac{3}{2000} & 44 \\\\\n", "{x}_{4} & 1 & 0 & \\frac{23}{48} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \\frac{1}{6000} & -\\frac{1}{18000} & 10 \\\\\n", "{\\color{green}{s}}_{3} & -3 & 0 & -\\frac{51}{10} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{1250} & \\frac{1}{1250} & 23 \\\\\n", "{x}_{2} & 0 & 1 & \\frac{9}{160} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{20000} & \\frac{19}{180000} & 6 \\\\\n", "{\\color{green}{s}}_{2} & 1 & 0 & \\frac{77}{48} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -\\frac{1}{1200} & \\frac{1}{3600} & 2 \\\\\n", "{\\color{green}{s}}_{8} & 0 & 0 & \\frac{815}{4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & -\\frac{7}{100} & -\\frac{3}{100} & 300 \\\\\n", "{\\color{green}{s}}_{6} & 5 & 0 & \\frac{21}{2} & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & \\frac{1}{250} & -\\frac{1}{250} & 20 \\\\\n", "{\\color{green}{s}}_{7} & 30 & 0 & \\frac{415}{4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & \\frac{1}{100} & -\\frac{3}{100} & 180 \\\\\n", "{\\color{green}{s}}_{5} & 0 & 0 & \\frac{5}{24} & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & -\\frac{1}{600} & \\frac{1}{1800} & 0 \\\\\n", "{\\color{green}{s}}_{9} & 0 & 0 & -\\frac{35}{4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -\\frac{17}{100} & \\frac{1}{300} & 0 \\\\\n", "{\\color{green}{s}}_{4} & 3 & 0 & \\frac{23}{6} & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & \\frac{1}{750} & -\\frac{1}{750} & 8 \\\\\n", "\\hline\n", " {Z_{ind}} & -3 & 0 & -\\frac{977}{240} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -\\frac{7}{30000} & -\\frac{1}{10000} & 32\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ B| x1 x2 x3 x4 s1 s2 s3 s4 s5 s6 s7 s8 s9 s10 s11| rhs]\n", "[---------+-----------------------------------------------------------------------------------------------------------------------------------------------------+---------]\n", "[ s1| 9 0 733/48 0 1 0 0 0 0 0 0 0 0 11/6000 -3/2000| 44]\n", "[ x4| 1 0 23/48 1 0 0 0 0 0 0 0 0 0 1/6000 -1/18000| 10]\n", "[ s3| -3 0 -51/10 0 0 0 1 0 0 0 0 0 0 -1/1250 1/1250| 23]\n", "[ x2| 0 1 9/160 0 0 0 0 0 0 0 0 0 0 -1/20000 19/180000| 6]\n", "[ s2| 1 0 77/48 0 0 1 0 0 0 0 0 0 0 -1/1200 1/3600| 2]\n", "[ s8| 0 0 815/4 0 0 0 0 0 0 0 0 1 0 -7/100 -3/100| 300]\n", "[ s6| 5 0 21/2 0 0 0 0 0 0 1 0 0 0 1/250 -1/250| 20]\n", "[ s7| 30 0 415/4 0 0 0 0 0 0 0 1 0 0 1/100 -3/100| 180]\n", "[ s5| 0 0 5/24 0 0 0 0 0 1 0 0 0 0 -1/600 1/1800| 0]\n", "[ s9| 0 0 -35/4 0 0 0 0 0 0 0 0 0 1 -17/100 1/300| 0]\n", "[ s4| 3 0 23/6 0 0 0 0 1 0 0 0 0 0 1/750 -1/750| 8]\n", "[---------+-----------------------------------------------------------------------------------------------------------------------------------------------------+---------]\n", "[ Z| -3 0 -977/240 0 0 0 0 0 0 0 0 0 0 -7/30000 -1/10000| 32]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cambio(11,8)" ] } ], "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 }