{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "cfd262a3-b18d-417a-a930-7ba5e8f48c57",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html>\\(\\displaystyle {===================================}\\)</html>"
      ],
      "text/latex": [
       "$\\displaystyle {===================================}$"
      ],
      "text/plain": [
       "ry"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<html>\\(\\displaystyle {===================================}\\)</html>"
      ],
      "text/latex": [
       "$\\displaystyle {===================================}$"
      ],
      "text/plain": [
       "ry"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<html>\\(\\displaystyle \\begin{array}{l}\n",
       "\\begin{array}{lcrcrcrcl}\n",
       " \\max \\mspace{-6mu}&\\mspace{-6mu}  \\mspace{-6mu}&\\mspace{-6mu} 50 x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 40 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 70 x_{3} \\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} 2 x_{2} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 3 x_{3} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 12 \\\\\n",
       " \\mspace{-6mu}&\\mspace{-6mu}  \\mspace{-6mu}&\\mspace{-6mu} 20 x_{1} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 10 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 30 x_{3} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 230 \\\\\n",
       " \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 100 x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 80 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 120 x_{3} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 1000 \\\\\n",
       "\\end{array} \\\\\n",
       "x_{1}, x_{2}, x_{3} \\geq 0\n",
       "\\end{array}\\)</html>"
      ],
      "text/latex": [
       "$\\displaystyle \\begin{array}{l}\n",
       "\\begin{array}{lcrcrcrcl}\n",
       " \\max \\mspace{-6mu}&\\mspace{-6mu}  \\mspace{-6mu}&\\mspace{-6mu} 50 x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 40 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 70 x_{3} \\mspace{-6mu}&\\mspace{-6mu}  \\mspace{-6mu}&\\mspace{-6mu} \\\\\n",
       " \\mspace{-6mu}&\\mspace{-6mu}  \\mspace{-6mu}&\\mspace{-6mu} x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{2} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 3 x_{3} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 12 \\\\\n",
       " \\mspace{-6mu}&\\mspace{-6mu}  \\mspace{-6mu}&\\mspace{-6mu} 20 x_{1} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 10 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 30 x_{3} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 230 \\\\\n",
       " \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 100 x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 80 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 120 x_{3} \\mspace{-6mu}&\\mspace{-6mu} \\leq \\mspace{-6mu}&\\mspace{-6mu} 1000 \\\\\n",
       "\\end{array} \\\\\n",
       "x_{1}, x_{2}, x_{3} \\geq 0\n",
       "\\end{array}$"
      ],
      "text/plain": [
       "LP problem (use 'view(...)' or '%display typeset' for details)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<html>\\(\\displaystyle \\frac{107660}{81}\\)</html>"
      ],
      "text/latex": [
       "$\\displaystyle \\frac{107660}{81}$"
      ],
      "text/plain": [
       "107660/81"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<html>\\(\\displaystyle \\left(\\frac{206}{27},\\,\\frac{109}{9},\\,\\frac{536}{81}\\right)\\)</html>"
      ],
      "text/latex": [
       "$\\displaystyle \\left(\\frac{206}{27},\\,\\frac{109}{9},\\,\\frac{536}{81}\\right)$"
      ],
      "text/plain": [
       "(206/27, 109/9, 536/81)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<html>\\(\\displaystyle {===================================}\\)</html>"
      ],
      "text/latex": [
       "$\\displaystyle {===================================}$"
      ],
      "text/plain": [
       "ry"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<html>\\(\\displaystyle {}\\)</html>"
      ],
      "text/latex": [
       "$\\displaystyle {}$"
      ],
      "text/plain": [
       "salto"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<html>\\(\\displaystyle {===================================}\\)</html>"
      ],
      "text/latex": [
       "$\\displaystyle {===================================}$"
      ],
      "text/plain": [
       "ry"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<html>\\(\\displaystyle \\left(\\begin{array}{r|rrrrrr|r}\n",
       "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {b} \\\\\n",
       "\\hline\n",
       " {\\color{green}{s}}_{1} & 1 & 2 & -3 & 1 & 0 & 0 & 12 \\\\\n",
       "{\\color{green}{s}}_{2} & 20 & -10 & 30 & 0 & 1 & 0 & 230 \\\\\n",
       "{\\color{green}{s}}_{3} & -100 & 80 & 120 & 0 & 0 & 1 & 1000 \\\\\n",
       "\\hline\n",
       " {Z_{ind}} & 50 & 40 & 70 & 0 & 0 & 0 & 0\n",
       "\\end{array}\\right)\\)</html>"
      ],
      "text/latex": [
       "$\\displaystyle \\left(\\begin{array}{r|rrrrrr|r}\n",
       "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {b} \\\\\n",
       "\\hline\n",
       " {\\color{green}{s}}_{1} & 1 & 2 & -3 & 1 & 0 & 0 & 12 \\\\\n",
       "{\\color{green}{s}}_{2} & 20 & -10 & 30 & 0 & 1 & 0 & 230 \\\\\n",
       "{\\color{green}{s}}_{3} & -100 & 80 & 120 & 0 & 0 & 1 & 1000 \\\\\n",
       "\\hline\n",
       " {Z_{ind}} & 50 & 40 & 70 & 0 & 0 & 0 & 0\n",
       "\\end{array}\\right)$"
      ],
      "text/plain": [
       "[   B|  x1   x2   x3   s1   s2   s3| rhs]\n",
       "[----+-----------------------------+----]\n",
       "[  s1|   1    2   -3    1    0    0|  12]\n",
       "[  s2|  20  -10   30    0    1    0| 230]\n",
       "[  s3|-100   80  120    0    0    1|1000]\n",
       "[----+-----------------------------+----]\n",
       "[   Z|  50   40   70    0    0    0|   0]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tipo='max'  # max o min\n",
    "\n",
    "n=3 #  número de variables x's\n",
    "m=3 #  número de restricciones (distintas de las de signo)\n",
    "\n",
    "c=matrix(QQ,1,n,[50,40,70] )  # vector de costos\n",
    "\n",
    "A=matrix(QQ,m,n,[   # coeficientes de las variables x's\n",
    "[1,2,-3],\n",
    "[20,-10,30],\n",
    "[-100,80,120]\n",
    "])\n",
    "\n",
    "b=matrix(QQ,m,1,[12,230,1000])  # vector de la derecha\n",
    "\n",
    "\n",
    "######################################################\n",
    "############### VARIABLES DE HOLGURA  ################\n",
    "\n",
    "\n",
    "h=matrix(ZZ,1,m,[1,1,1])  # variables de holgura: \n",
    "                            # Pon 1 si va sumando, \n",
    "                            # -1 si va restando y \n",
    "                            # 0 si no hay variable de holgura.\n",
    "t=matrix(ZZ,1,m,[0,0,0])\n",
    "\n",
    "colId=(4,5,6)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "####################################################################\n",
    "############  HASTA AQUÍ LOS DATOS  ################################\n",
    "####################################################################\n",
    "\n",
    "\n",
    "\n",
    "load('https://sage.unex.es/501708/simplex2023CompletamenteManual.sage')\n",
    "\n",
    "#load('https://sage.unex.es/501708/simplex2023Auto.sage')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "d37894b7-7b7a-46fb-83e9-cfa5a60c491e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html>\\(\\displaystyle \\left(\\begin{array}{r|rrrrrr|r}\n",
       "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {b} \\\\\n",
       "\\hline\n",
       " {x}_{2} & \\frac{1}{2} & 1 & -\\frac{3}{2} & \\frac{1}{2} & 0 & 0 & 6 \\\\\n",
       "{\\color{green}{s}}_{2} & 25 & 0 & 15 & 5 & 1 & 0 & 290 \\\\\n",
       "{\\color{green}{s}}_{3} & -140 & 0 & 240 & -40 & 0 & 1 & 520 \\\\\n",
       "\\hline\n",
       " {Z_{ind}} & 30 & 0 & 130 & -20 & 0 & 0 & 240\n",
       "\\end{array}\\right)\\)</html>"
      ],
      "text/latex": [
       "$\\displaystyle \\left(\\begin{array}{r|rrrrrr|r}\n",
       "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {b} \\\\\n",
       "\\hline\n",
       " {x}_{2} & \\frac{1}{2} & 1 & -\\frac{3}{2} & \\frac{1}{2} & 0 & 0 & 6 \\\\\n",
       "{\\color{green}{s}}_{2} & 25 & 0 & 15 & 5 & 1 & 0 & 290 \\\\\n",
       "{\\color{green}{s}}_{3} & -140 & 0 & 240 & -40 & 0 & 1 & 520 \\\\\n",
       "\\hline\n",
       " {Z_{ind}} & 30 & 0 & 130 & -20 & 0 & 0 & 240\n",
       "\\end{array}\\right)$"
      ],
      "text/plain": [
       "[   B|  x1   x2   x3   s1   s2   s3| rhs]\n",
       "[----+-----------------------------+----]\n",
       "[  x2| 1/2    1 -3/2  1/2    0    0|   6]\n",
       "[  s2|  25    0   15    5    1    0| 290]\n",
       "[  s3|-140    0  240  -40    0    1| 520]\n",
       "[----+-----------------------------+----]\n",
       "[   Z|  30    0  130  -20    0    0| 240]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cambio(1,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "e859d5b1-2619-4908-b8d0-7f237c92251d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[    NO]\n",
       "[19.333]\n",
       "[2.1667]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cocientes(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "3bfa1942-6489-4c34-acf4-b7192548cf16",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html>\\(\\displaystyle \\left(\\begin{array}{r|rrrrrr|r}\n",
       "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {b} \\\\\n",
       "\\hline\n",
       " {x}_{2} & -\\frac{3}{8} & 1 & 0 & \\frac{1}{4} & 0 & \\frac{1}{160} & \\frac{37}{4} \\\\\n",
       "{\\color{green}{s}}_{2} & \\frac{135}{4} & 0 & 0 & \\frac{15}{2} & 1 & -\\frac{1}{16} & \\frac{515}{2} \\\\\n",
       "{x}_{3} & -\\frac{7}{12} & 0 & 1 & -\\frac{1}{6} & 0 & \\frac{1}{240} & \\frac{13}{6} \\\\\n",
       "\\hline\n",
       " {Z_{ind}} & \\frac{635}{6} & 0 & 0 & \\frac{5}{3} & 0 & -\\frac{13}{24} & \\frac{1565}{3}\n",
       "\\end{array}\\right)\\)</html>"
      ],
      "text/latex": [
       "$\\displaystyle \\left(\\begin{array}{r|rrrrrr|r}\n",
       "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {\\color{green}{s}}_{1} & {\\color{green}{s}}_{2} & {\\color{green}{s}}_{3} & {b} \\\\\n",
       "\\hline\n",
       " {x}_{2} & -\\frac{3}{8} & 1 & 0 & \\frac{1}{4} & 0 & \\frac{1}{160} & \\frac{37}{4} \\\\\n",
       "{\\color{green}{s}}_{2} & \\frac{135}{4} & 0 & 0 & \\frac{15}{2} & 1 & -\\frac{1}{16} & \\frac{515}{2} \\\\\n",
       "{x}_{3} & -\\frac{7}{12} & 0 & 1 & -\\frac{1}{6} & 0 & \\frac{1}{240} & \\frac{13}{6} \\\\\n",
       "\\hline\n",
       " {Z_{ind}} & \\frac{635}{6} & 0 & 0 & \\frac{5}{3} & 0 & -\\frac{13}{24} & \\frac{1565}{3}\n",
       "\\end{array}\\right)$"
      ],
      "text/plain": [
       "[     B|    x1     x2     x3     s1     s2     s3|   rhs]\n",
       "[------+-----------------------------------------+------]\n",
       "[    x2|  -3/8      1      0    1/4      0  1/160|  37/4]\n",
       "[    s2| 135/4      0      0   15/2      1  -1/16| 515/2]\n",
       "[    x3| -7/12      0      1   -1/6      0  1/240|  13/6]\n",
       "[------+-----------------------------------------+------]\n",
       "[     Z| 635/6      0      0    5/3      0 -13/24|1565/3]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cambio(3,3)"
   ]
  }
 ],
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