{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "395f917b-a519-4d11-be85-bd4f9870521f",
   "metadata": {},
   "source": [
    "# Bank loans\n",
    "\n",
    "A bank plans its loan policy. The total budget is up to $12 milion.\n",
    "The possible loan types are:\n",
    "\n",
    "| loan type | interest | risk |\n",
    "|-----------|--------|-----|\n",
    "| Personal  | .140   | .10 |\n",
    "| Car       | .130   | .07 |\n",
    "| Household | .120   | .03 |\n",
    "| Farms     | .125   | .05 |\n",
    "| Bussiness | .100   | .02 |\n",
    "\n",
    "\n",
    "To simplify the calculations, we assume that the risk loans will not payback anything.\n",
    "Due to regulation, at least 40% of allocated money but go to farms or bussiness projects.\n",
    "Due to regional policy, the household loans must be at least half of money allocated\n",
    "to household, personal and car loans.\n",
    "To avoid the whole poject being too risky, the risk loans must be at most 4% of all loans.\n",
    "How should the bank set the loan policy to maximize its earnings."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "adf77c68-4ee8-4410-8941-0466c405c9f5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(12996480.0, {0: 0.0, 1: 0.0, 2: 7200000.0, 3: 0.0, 4: 4800000.0})"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = [\n",
    "    (\"personal\", .140, 0.1),\n",
    "    (\"car\"     , .130, 0.07),\n",
    "    (\"house\"   , .120, 0.03),\n",
    "    (\"farms\"   , .125, 0.05),\n",
    "    (\"bussiness\",.100, 0.02),\n",
    "]\n",
    "P = MixedIntegerLinearProgram(maximization=True)\n",
    "x = P.new_variable(nonnegative=True, integer=True)\n",
    "s = P.sum( x[i] for i in range(len(data)) )\n",
    "P.add_constraint(s <= 12_000_000)\n",
    "P.add_constraint(x[3] + x[4] >= 0.4 * s)\n",
    "P.add_constraint(x[2] >= 0.5*(x[2] + x[0] + x[1]))\n",
    "P.add_constraint(P.sum( data[i][2]*x[i] for i in range(len(data)) ) <= 0.04*s)\n",
    "P.set_objective(P.sum( (1-data[i][2])*(1 + data[i][1])*x[i] for i in range(len(data)) ))\n",
    "sol = P.solve()\n",
    "sol, P.get_values(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f3dc8635-0bed-4ee2-9604-de353f2cb56d",
   "metadata": {},
   "source": [
    "# Point separation\n",
    "You are given two sets of points: black and red. You task is to find a line which separates black and red points.\n",
    "You may assume that line parallel with y-axis is never a solution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "88a1b78d-8cdc-44fc-b969-bf1954458687",
   "metadata": {},
   "outputs": [],
   "source": [
    "point_sets = [\n",
    "    {\"black\":[\n",
    "        [-18696,-7622],[-9507,2766],[-606,-12929],[-18153,13773],[-13849,-9818],[-15036,-10614],[-12732,-7760],[279,-11867],\n",
    "        [-19409,-5654],[-12110,859],[-5654,-17544],[-15400,12070],[-18373,-595],[-11888,-9372],[-17018,-13533],[-1884,-16962],\n",
    "        [-15963,2086],[-15130,-10194],[-17569,1064],[-19089,-11955],[-19637,1385],[-10732,-16074],[-5827,-12756],[-14789,1622],\n",
    "        [-19944,14320],[-13649,719],[-5736,-2697],[-3723,-12397],[-11766,-16796],[-14917,4362],[-11841,-6097],[-11642,-14858],\n",
    "        [-13850,639],[-5022,-4003],[-19551,-2751],[828,-16459],[-18063,-8444],[-7817,-622],[-9619,1626],[-3450,-19773],\n",
    "        [-4199,-18748],[-18371,9045],[-15438,12680]],\n",
    "     \"red\":[\n",
    "         [7284,15539],[13473,293],[8473,14157],[-5670,19128],[2053,16099],[10337,10526],[-6853,17759],[18704,17951],\n",
    "         [-2487,602],[-6388,17862],[9428,15933],[2243,-12127],[2886,-2748],[3595,4590],[4614,-3431],[-3214,-2094],\n",
    "         [-6271,19367],[12794,-8700],[7094,-223],[15730,-18544],[-3835,435],[12570,-18044],[2493,-1457],[6835,14932],\n",
    "         [-8395,7125],[15272,11036],[-4613,8504],[17527,-2778],[-4598,6043],[17656,14510],[4441,-2122],[4584,17428],\n",
    "         [-1340,4434],[14283,17595],[-540,-2763],[-8191,16686],[11907,18450],[17978,17080],[9342,18405],[-4758,-1364],\n",
    "         [-10570,17455],[14552,-11267],[11775,710],[-15804,19376],[5246,9032],[272,3172],[16984,-5459],[-6234,14116],\n",
    "         [11816,4257],[-5189,11859],[13932,8569],[10491,16115],[-1652,-729],[7575,2600],[19456,6872],[18124,-845],[7689,8963]]},\n",
    "    {\"black\":[\n",
    "        [-17834,-11695],[10712,-4403],[-9730,-15197],[14497,-17228],[10492,-3716],[-9842,76],[-14368,-3871],[-10594,-12605],\n",
    "        [-6731,1050],[-10894,-13136],[4606,-5753],[-7580,2682],[-5887,-10916],[-16721,-10177],[-6878,5235],[3083,-19450],\n",
    "        [6992,638],[-12630,-18791],[13334,-15892],[9294,4009],[19120,-19868],[-16291,1389],[16913,-13516],[7471,366],\n",
    "        [-1657,4306],[1323,-14827],[-6471,-17177],[-10592,7094],[-10164,12742],[18675,-19616],[-17629,-2120],[13553,1785],\n",
    "        [16798,-15206],[13419,-9147],[-1702,-698],[10902,-12855],[-12115,-13001],[7084,-11798],[-17468,-5476],[55,-2715],\n",
    "        [-16456,12676],[2456,-14728],[-9105,9070],[-18701,-10687],[19200,-11367],[-15566,6248],[-4694,-8210],[-11360,8829],\n",
    "        [-14475,-1192],[-10819,-2872],[-3178,1196],[-8672,-15120],[-13984,11799],[-10689,-1594],[-13413,-7767],[-17662,-1124],\n",
    "        [7892,1935],[-14313,-9545],[12570,167],[6790,-10557],[14095,1294],[-5453,-4826],[6868,-1101],[-8814,-12038],[9609,-18823],\n",
    "        [-252,-12704],[-17804,-17802],[-13226,6394],[-8711,3024],[133,-17361],[13230,-15564],[-10708,668],[-1135,-9515],\n",
    "        [6946,-15399],[19064,2232],[-4457,4621],[-19398,540]],\n",
    "     \"red\":[\n",
    "         [18024,14535],[2694,10943],[1475,16887],[-15317,19284],[7856,10793],[10615,8656],[14717,12152],[-8057,13397],[893,15988],\n",
    "         [576,14494],[17866,15425],[15884,5805],[14422,11145],[-6168,18823],[15264,14777],[15408,9232],[-7401,17631],\n",
    "         [-14948,16505],[17165,14173],[15648,8631],[11912,10260],[-5847,18580],[18253,6089]]},\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "aed44bef-4836-4c8c-9e17-a2810b231a65",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_points(pts, c): return sum( point(p, color=c) for p in pts )\n",
    "def plot_sol(inp, a = 1, b = 1):\n",
    "    x = var(\"x\")\n",
    "    clip = 20000\n",
    "    return plot_points(inp[\"black\"], \"black\") + plot_points(inp[\"red\"], \"red\") + plot(a*x+b, xmin=-clip, xmax=clip, ymin=-clip, ymax=clip)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "40dd8d37-a9d1-4b70-8997-c664e164d78e",
   "metadata": {},
   "outputs": [],
   "source": [
    "black = point_sets[0][\"black\"]\n",
    "red = point_sets[0][\"red\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "1fc79977-f35f-46ce-b11f-29326b285cff",
   "metadata": {},
   "outputs": [],
   "source": [
    "def separate_points(black, red):\n",
    "    P2 = MixedIntegerLinearProgram(maximization=True)\n",
    "    xx = P2.new_variable()\n",
    "    a, b, eps = xx[0], xx[1], xx[2]\n",
    "    for px, py in red:\n",
    "        P2.add_constraint(a*px + b + eps <= py)\n",
    "    for px, py in black:\n",
    "        P2.add_constraint(a*px + b >= eps + py)\n",
    "    P2.add_constraint(eps >= 0)\n",
    "    P2.set_objective(eps)\n",
    "    sol = P2.solve()\n",
    "    return sol, P2.get_values(a), P2.get_values(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "c02f1f12-ed62-480c-a04d-5a8c62bbe85b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1318.0763504485592, -1.5618120506457975, -10113.17808742126)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eps, a, b = separate_points(point_sets[0][\"black\"], point_sets[0][\"red\"]); eps, a, b"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "291dce2e-37ec-4a50-b446-f9f33be0b6f2",
   "metadata": {},
   "source": [
    "Value of the objective function describes how well are the points separated. If it is negative, it was not possible to separate the points either because it is not possible at all or because we guessed wrong whether red ones should be above the line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "86538bc0-c8cf-4e7d-a114-4e6160f791f5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Graphics object consisting of 101 graphics primitives"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_sol(point_sets[0], a, b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "abda72a7-c077-4fe0-9c8e-01458bc01b97",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(706.3245860134081, -0.3595866976871495, 9793.48539072123)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eps, a, b = separate_points(point_sets[1][\"black\"], point_sets[1][\"red\"]); eps, a, b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "8f4e18d3-9465-4517-bdeb-08bbb4b6826d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Graphics object consisting of 101 graphics primitives"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_sol(point_sets[1], a, b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5572d48f-03a2-42ae-b6a9-f567a254e3a6",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "SageMath 10.2",
   "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": "3.11.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
