{
 "cells": [
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   "cell_type": "code",
   "execution_count": 15,
   "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}{lcrcrcrcrcrcl}\n",
       " \\min \\mspace{-6mu}&\\mspace{-6mu}  \\mspace{-6mu}&\\mspace{-6mu} 3 x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{3} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 2 x_{4} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{5} \\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} 2 x_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 3 x_{4} \\mspace{-6mu}&\\mspace{-6mu}  \\mspace{-6mu}&\\mspace{-6mu}  \\mspace{-6mu}&\\mspace{-6mu} = \\mspace{-6mu}&\\mspace{-6mu} 8 \\\\\n",
       " \\mspace{-6mu}&\\mspace{-6mu}  \\mspace{-6mu}&\\mspace{-6mu}  \\mspace{-6mu}&\\mspace{-6mu}  \\mspace{-6mu}&\\mspace{-6mu} x_{2} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 2 x_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{4} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{5} \\mspace{-6mu}&\\mspace{-6mu} = \\mspace{-6mu}&\\mspace{-6mu} 10 \\\\\n",
       "\\end{array} \\\\\n",
       "x_{1}, x_{2}, x_{3}, x_{4}, x_{5} \\geq 0\n",
       "\\end{array}\\)</html>"
      ],
      "text/latex": [
       "$\\displaystyle \\begin{array}{l}\n",
       "\\begin{array}{lcrcrcrcrcrcl}\n",
       " \\min \\mspace{-6mu}&\\mspace{-6mu}  \\mspace{-6mu}&\\mspace{-6mu} 3 x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{3} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 2 x_{4} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{5} \\mspace{-6mu}&\\mspace{-6mu}  \\mspace{-6mu}&\\mspace{-6mu} \\\\\n",
       " \\mspace{-6mu}&\\mspace{-6mu}  \\mspace{-6mu}&\\mspace{-6mu} x_{1} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{2} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 3 x_{4} \\mspace{-6mu}&\\mspace{-6mu}  \\mspace{-6mu}&\\mspace{-6mu}  \\mspace{-6mu}&\\mspace{-6mu} = \\mspace{-6mu}&\\mspace{-6mu} 8 \\\\\n",
       " \\mspace{-6mu}&\\mspace{-6mu}  \\mspace{-6mu}&\\mspace{-6mu}  \\mspace{-6mu}&\\mspace{-6mu}  \\mspace{-6mu}&\\mspace{-6mu} x_{2} \\mspace{-6mu}&\\mspace{-6mu} - \\mspace{-6mu}&\\mspace{-6mu} 2 x_{3} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} 2 x_{4} \\mspace{-6mu}&\\mspace{-6mu} + \\mspace{-6mu}&\\mspace{-6mu} x_{5} \\mspace{-6mu}&\\mspace{-6mu} = \\mspace{-6mu}&\\mspace{-6mu} 10 \\\\\n",
       "\\end{array} \\\\\n",
       "x_{1}, x_{2}, x_{3}, x_{4}, x_{5} \\geq 0\n",
       "\\end{array}$"
      ],
      "text/plain": [
       "LP problem (use 'view(...)' or '%display typeset' for details)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<html>\\(\\displaystyle 4\\)</html>"
      ],
      "text/latex": [
       "$\\displaystyle 4$"
      ],
      "text/plain": [
       "4"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<html>\\(\\displaystyle \\left(0,\\,0,\\,0,\\,\\frac{8}{3},\\,\\frac{14}{3}\\right)\\)</html>"
      ],
      "text/latex": [
       "$\\displaystyle \\left(0,\\,0,\\,0,\\,\\frac{8}{3},\\,\\frac{14}{3}\\right)$"
      ],
      "text/plain": [
       "(0, 0, 0, 8/3, 14/3)"
      ]
     },
     "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|rrrrr|r}\n",
       "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {b} \\\\\n",
       "\\hline\n",
       " {x}_{1} & 1 & 2 & 2 & 3 & 0 & 8 \\\\\n",
       "{x}_{5} & 0 & 1 & -2 & 2 & 1 & 10 \\\\\n",
       "\\hline\n",
       " {Z_{ind}} & 0 & -6 & -1 & -15 & 0 & 44\n",
       "\\end{array}\\right)\\)</html>"
      ],
      "text/latex": [
       "$\\displaystyle \\left(\\begin{array}{r|rrrrr|r}\n",
       "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {b} \\\\\n",
       "\\hline\n",
       " {x}_{1} & 1 & 2 & 2 & 3 & 0 & 8 \\\\\n",
       "{x}_{5} & 0 & 1 & -2 & 2 & 1 & 10 \\\\\n",
       "\\hline\n",
       " {Z_{ind}} & 0 & -6 & -1 & -15 & 0 & 44\n",
       "\\end{array}\\right)$"
      ],
      "text/plain": [
       "[  B| x1  x2  x3  x4  x5|rhs]\n",
       "[---+-------------------+---]\n",
       "[ x1|  1   2   2   3   0|  8]\n",
       "[ x5|  0   1  -2   2   1| 10]\n",
       "[---+-------------------+---]\n",
       "[  Z|  0  -6  -1 -15   0| 44]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tipo='min'  # max o min\n",
    "\n",
    "n=5 #  número de variables x's\n",
    "m=2 #  número de restricciones (distintas de las de signo)\n",
    "\n",
    "c=matrix(QQ,1,n,[3, 2, 1, -2, 2] )  # vector de costos\n",
    "\n",
    "A=matrix(QQ,m,n,[   # coeficientes de las variables x's\n",
    "[1,2,2,3,0],\n",
    "[0,1,-2,2,1]\n",
    "])\n",
    "\n",
    "b=matrix(QQ,m,1,[8,10])  # vector de la derecha\n",
    "\n",
    "\n",
    "######################################################\n",
    "############### VARIABLES DE HOLGURA  ################\n",
    "\n",
    "\n",
    "h=matrix(ZZ,1,m,[0,0])  # variables de holgura: \n",
    "                            # Pon 1 si va sumando, \n",
    "                            # -1 si va restando y \n",
    "                            # 0 si no hay variable de holgura.\n",
    "t=matrix(ZZ,1,m,[0,0])\n",
    "\n",
    "colId=(1,5)\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": 16,
   "id": "1dc94701-d11c-479d-b458-6bea5ddd8b92",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html>\\(\\displaystyle \\left(\\begin{array}{r|rrrrr|r}\n",
       "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {b} \\\\\n",
       "\\hline\n",
       " {x}_{2} & \\frac{1}{2} & 1 & 1 & \\frac{3}{2} & 0 & 4 \\\\\n",
       "{x}_{5} & -\\frac{1}{2} & 0 & -3 & \\frac{1}{2} & 1 & 6 \\\\\n",
       "\\hline\n",
       " {Z_{ind}} & 3 & 0 & 5 & -6 & 0 & 20\n",
       "\\end{array}\\right)\\)</html>"
      ],
      "text/latex": [
       "$\\displaystyle \\left(\\begin{array}{r|rrrrr|r}\n",
       "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {b} \\\\\n",
       "\\hline\n",
       " {x}_{2} & \\frac{1}{2} & 1 & 1 & \\frac{3}{2} & 0 & 4 \\\\\n",
       "{x}_{5} & -\\frac{1}{2} & 0 & -3 & \\frac{1}{2} & 1 & 6 \\\\\n",
       "\\hline\n",
       " {Z_{ind}} & 3 & 0 & 5 & -6 & 0 & 20\n",
       "\\end{array}\\right)$"
      ],
      "text/plain": [
       "[   B|  x1   x2   x3   x4   x5| rhs]\n",
       "[----+------------------------+----]\n",
       "[  x2| 1/2    1    1  3/2    0|   4]\n",
       "[  x5|-1/2    0   -3  1/2    1|   6]\n",
       "[----+------------------------+----]\n",
       "[   Z|   3    0    5   -6    0|  20]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cambio(1,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "113c0ab7-714b-4df6-b3f1-ba6fb3f4b8bb",
   "metadata": {},
   "outputs": [],
   "source": [
    "#cambio(1,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "e3c9ca5d-5f58-4579-8e3f-5e51fef10d3d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html>\\(\\displaystyle \\left(\\begin{array}{r|rrrrr|r}\n",
       "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {b} \\\\\n",
       "\\hline\n",
       " {x}_{4} & \\frac{1}{3} & \\frac{2}{3} & \\frac{2}{3} & 1 & 0 & \\frac{8}{3} \\\\\n",
       "{x}_{5} & -\\frac{2}{3} & -\\frac{1}{3} & -\\frac{10}{3} & 0 & 1 & \\frac{14}{3} \\\\\n",
       "\\hline\n",
       " {Z_{ind}} & 5 & 4 & 9 & 0 & 0 & 4\n",
       "\\end{array}\\right)\\)</html>"
      ],
      "text/latex": [
       "$\\displaystyle \\left(\\begin{array}{r|rrrrr|r}\n",
       "{Basic} & {x}_{1} & {x}_{2} & {x}_{3} & {x}_{4} & {x}_{5} & {b} \\\\\n",
       "\\hline\n",
       " {x}_{4} & \\frac{1}{3} & \\frac{2}{3} & \\frac{2}{3} & 1 & 0 & \\frac{8}{3} \\\\\n",
       "{x}_{5} & -\\frac{2}{3} & -\\frac{1}{3} & -\\frac{10}{3} & 0 & 1 & \\frac{14}{3} \\\\\n",
       "\\hline\n",
       " {Z_{ind}} & 5 & 4 & 9 & 0 & 0 & 4\n",
       "\\end{array}\\right)$"
      ],
      "text/plain": [
       "[    B|   x1    x2    x3    x4    x5|  rhs]\n",
       "[-----+-----------------------------+-----]\n",
       "[   x4|  1/3   2/3   2/3     1     0|  8/3]\n",
       "[   x5| -2/3  -1/3 -10/3     0     1| 14/3]\n",
       "[-----+-----------------------------+-----]\n",
       "[    Z|    5     4     9     0     0|    4]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cambio(1,4)"
   ]
  }
 ],
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