{
 "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": null,
   "id": "adf77c68-4ee8-4410-8941-0466c405c9f5",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "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": 15,
   "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": 13,
   "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": 17,
   "id": "d4f0e538-db46-4ecc-899e-23040be4181d",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "Graphics object consisting of 101 graphics primitives"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_sol(point_sets[1], -3, 12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "40dd8d37-a9d1-4b70-8997-c664e164d78e",
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