{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{align*}\n",
    "-x &\\le 0 \\\\\n",
    "-y &\\le 0 \\\\\n",
    "x + y &\\le 1 \\\\[1ex]\n",
    "a_i x + b_i y &\\le c_i\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = [-1, 0, 1]\n",
    "b = [0, -1, 1]\n",
    "c = [0, 0, 1]\n",
    "tocke = [(1, 2), (3, -2), (4, 0)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = MixedIntegerLinearProgram(maximization=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.2000000000004"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p.set_objective(p['k'])\n",
    "for xi, yi in tocke:\n",
    "    for ai, bi, ci in zip(a, b, c):\n",
    "        p.add_constraint(ai * (p['k'] * xi + p['x']) + bi * (p['k'] * yi + p['y']) <= ci)\n",
    "p.solve()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.2000000000004, -0.20000000000039997, 0.3999999999988)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k, x, y = p.get_values(p['k']), p.get_values(p['x']), p.get_values(p['y'])\n",
    "k, x, y"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "SageMath 9.2.rc2",
   "language": "sage",
   "name": "sagemath"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.10"
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 "nbformat": 4,
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}