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@thiakx
Last active August 29, 2015 14:13
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{
"metadata": {
"name": "",
"signature": "sha256:461b10d5e75c36757ca3fd9450678c33ba1def215cc3977ee01b59a2c391d6b6"
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"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Simple Optimization with Python - PyData SG Meetup\n",
"by Kai Xin [@thiakx](https://twitter.com/thiakx)"
]
},
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Part 0 - Loading the Libs"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%matplotlib inline\n",
"import numpy as np\n",
"import pylab as pl\n",
"import seaborn as sns\n",
"import pulp\n",
"from scipy import stats\n",
"from scipy import optimize\n",
"from matplotlib import pyplot as plt\n",
"from matplotlib.path import Path\n",
"from matplotlib.patches import PathPatch\n",
"from mpl_toolkits.mplot3d import Axes3D\n",
"from matplotlib import cm\n",
"from matplotlib.colors import LogNorm"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Part I - 4 basic steps of framing an optimization problem."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Reference: http://scipy-lectures.github.io/advanced/mathematical_optimization/"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Step1: Identify if problem is convex or non-convex.**"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\"\"\"\n",
"Definition of a convex function\n",
"\"\"\"\n",
"x = np.linspace(-1, 2)\n",
"\n",
"pl.figure(1, figsize=(5, 5))\n",
"\n",
"# A convex function\n",
"pl.plot(x, x**2, linewidth=2)\n",
"pl.text(-.7, -.6**2, '$f$', size=20)\n",
"\n",
"# The tangent in one point\n",
"pl.text(.1, -.75, \"Convex problem, one optimal solution\", size=15)\n",
"pl.text(0, -0.1, 'X', size=15)\n",
"\n",
"# Convexity as barycenter\n",
"pl.ylim(ymin=-1)\n",
"pl.axis('off')\n",
"pl.tight_layout()\n",
"\n",
"# Convexity as barycenter\n",
"pl.figure(2, figsize=(5, 5))\n",
"pl.clf()\n",
"pl.plot(x, x**2 + np.exp(-5*(x - .5)**2), linewidth=2)\n",
"pl.text(-.7, -.6**2, 'Non convex problem, many local minima and one global minimum', size=15)\n",
"\n",
"pl.ylim(ymin=-1)\n",
"pl.axis('off')\n",
"pl.tight_layout()\n",
"pl.show()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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lnt4QuSSRpqAWmUgFJFmxPHBRWPylQkykw5AGWZIVnx3KxxNpBUlWLARcAcyDTQp8VNyK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\n3ztfuZHsZwAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x108ac5310>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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PWwjsEWM8rpm+nLSOnEFav9YCzgLe3zzHoaT35zpg5xjjzc3jtiBtAxsMPP/l\nwG0xxh0G6ipI79kzgQuB3YA1SO//FqTl/G8xxp+MtrzmY1fUIlLz2g2kVpsRhRBWB64m7XT/vbnv\naxh5oz4cWAi8C/gOcABpIx1VCGHb5rl+D+wMvIO0w+vtEJ8DfA/4G7AT6U19JzDSTu1k0gfIO5vX\ndVwIYZPmf+c1r3mwdWpH4E/At5r5bQ18k7SC/yspXBTNayPG+Ktm+kNN4AL4COnD6+3jhTjSzhPg\n34AzgaNCCO8euM9KpI3mLOD1wNUhhFeRVu7/A3YATgUOHqVP/Nzm9ewE/Bq4IISw4WgFhRDWBK4F\nHk/aeHYnfdCOtNM5sbnvHqQPodObHdrqpA37f4CjQwgvGH0RjOlw4C7Sjuou4AshhP1JO/wPkt7H\nfUjvTc9apHXmvaTgWAGHNdODxlpHLgL+AOwy8Ji3k9aRr0/0RYQQdiW9R5c1NV0EnNQ/FiaEsA7w\nI9KHzQdIH2znAWs3d1mJ9KVrf1IQPp4UyB4RjibhfcCTgT1JHyzHhxD2JW3XHyO9t28lfQCNZyLb\n+kjbwlTWn3VJ+4BdgTeRPshOCyFsM06Nk3ncmaT3ajfSendGCOEpvX+GEPYghczTSdvuMizelkc1\nnfvPSW6n/TU8nxTYI2mfcAVwTvPvUfdX07zPWY/Urfk20nL4BXBhCOG5Y9U+ihVJ28AppGW0GWm9\n+iJpe9qd9KXx7BDCin2PG+xqW0Ta1o4FPk0KKeuS1oVBg497Puk9OLCZ726k9+940hfhDwPrN3WN\nZ6S61iHtw44ifQb1utFOBb5B2lZWIX1OjGo+ttgsaFogDgNODiEcEGO8YYT7FaQNKYsx3g4QQrgd\n+HoIYduBbzW/76Vh4KIQwlaknfpY/ZMlcF6M8S19t/V/K96f1BKSxxgXNvNfivSB9C8xxh/23ff7\nMcaPN/f5NnBHM/+rY4x3NYOldwQ+3/eYHYGz+wLJ0cC3Yoy7N9OXhhDWAD4YQvhEjPH2GONnm0B2\nagjhP0gbxB793/LHcGeMsRdkLgkhrE/aCI7vu8+KpG/lDy+HEMIXgB/HGN/R3HRxCGE14H0hhKNi\njLf0Pf7CGOPRzeMuBm5tanzzKDUdTAr3r48x3ts87s/A5SGE18UYL+i773djjGVzn+uBnwKvizE+\nu7mtFw62A6bShPurGONHmue6nNRlWgBPjDH+g7RebUwKqGcCNC1tvda2BaRg+jhSsPn0wPOPtY4s\nbL4t7dL9xm8SAAAL2klEQVQsk97z7QKc1lv/xtOsnwcD5/dtD5c239wPDCF8tmltPIT0IfrSvq7G\nh7/lNt1Au/U973dI39LOCiGsEWO8dSL19PlHb90LIVxIep8OA9Zs1p+vN61T29IE+TFMZFsfqVth\n0utPjPHhnXfzflxEamF5L+nDckSTfNz5fd/If076YrMNcEIIYWnS9vOVGOMBzf0vCSH8kPHHhEzn\n/nMy22m/fYGfxxh72//FTSvzeO/xIUzTPqe3bJv/LyB9+diI9AVm8IvdeFYCjokxntk83yLgOOAz\nfTX8lLRubU5630eyAHgSsEOM8bvN45YCPhVCCDHGOMbjngpsGmP8E+m9XI/05eRNMcazmueC9Dm1\nQozxvjFez+B2soDUMpPHGK8CvhpCWAXYG/hgjPHE5vn/3Mx71FrnY4tNz5eA35JWwp7+Bf0C4Nre\nRtm4gtSUPfitfHBncSWLv30+SvONaD3G/gb6AuDygQ+V3redTQbu+/D8m2benwBP6fv/mcArQgir\nNvP/Z1JLS28DWbOZ/kIIYZneD+lbywrABn3P9e+kloJvApfFGE8Y4zX0u2xg+nJgrRBC/3Ja1MyT\npq6lSU2ug9/yLgGWI3XRjTiPJrB9m0e/V/02J+08H+h7zd8nfegPDi6/sO/vG5vfD+84mvndRFo2\nU/Hw8zfv4a2k5fuPgfn2f5teIYRwcAjhl6Rvag+QPrzWG+H5x1tHTgHWbZqNIXUJPpXJtZKsTeoy\nG+n9Wg34f830S4Az4xjjp0IIbwshXBtC+CvpdZ3V/OufJlFPT/+yXUQKSdcNfEA9YtmOYVLb+kg1\nMMH1J4TwhBDCJ0MIvyEtgweArVm8HEc0ycf1v56fkdb93nJYh9TSdfnAYy5j/DEh07n/nMx22m8T\nHvllkRGmH2G69zkhhLVDCKeGEG4GHiJ1G23IOO/hKBaSuuB6HrUe9d023n7odtJy7un9Pd428KMm\n1PTPb7S6prIv/AuP/GI41msctdZ5G2xijA+RmljfGkY+bPHJwA8HHvN3UvPk4Bv2i4Hpu0iBYDS9\njfaPY9xnpPnfANw9hfnXwIPA9s30jsDvYoy9lXmd5vepLN4RPkAa89NrtuzV8Afgu6T+9v7WlvFc\nNzB9bfN7zb7b7mjel57VgGUZWA7ANc3vweUwOI/rBp5/0DqkoPYgi1/zPaSmzsEPq1/2/ogxPjB4\nW+NBxn7fxzL4XA+Mclv/8x9OCuafIXXVPJ/UtbJ8ePRhqGOuI01X4+WkLlGa31fFGH8+idfQW9bj\nvV9PYYx1v9cqCPyA1CXxQhZ3pa4yiXp6prJsRzPZbf1RNUxi/fk8qQvjcOCVpPf3FGDVceY1mcc9\n/HqaD+a7+2p4cvN7cPDp4HY2kuncf05mO+33JNKYkH7jHVY9bfucphXkfFIw2580PmQTUsgd7z0c\nyR0xxjv6ph+1HvWtW+OtkzcNDB+4c4KPG2m7uSPGeOfAbRN5rpH8aqCukbaVcZ9/PnZF9TuFNE5k\nXx7dtPpH4Hn9N4QQHkPqPxyt6XOibm5+r8WjN6Cx5v8MUlfDpI66iDH+LYTwdVKgOZE0TqO/6bz3\nfO9kceDo9+u+GrYlffu7DjgyhHBxr3l4HBvzyPFBGze/+z/gBt+DP5N2Zs8beGzvW9rgctiY1Jw/\n2vSgm0nfzE4a4X+TPiKmBTsA58QYHx7zEELIluD5TgJODCF8iNQV8P5JPr73Xj6PNMajZ/D9upmx\nv83t0NznXX3dsJtPspY5LYSwAqlL6IgY43/33b70TDxuFL1v5huRxgD1bDzCfQdN5/5zqtvpn0hd\nG/1WH2de07nP+SdSC8+7Y9/g+eZLR9uHl8/mEaK97qjH925ouuWeSWqZ7jctdc3bFht4ON0eRRoU\nN/jN/ipgo173TeNlpDR/1QSeftQVN6ZDQm/k0YM1B+e/RZP6e7Zqfo83hmOkeZ8BbN588D2NvsFX\nTT03AU+LMf5whJ9eH/lqpNaB40gtBKsyfn91z8sHprcE/tAbOT+SphvmGuAVA//aitSkO/ht6eF5\nNMttcx65rAaXy3dII/VHes2/HfcVPdps76xWIDUpAw9/eL1pgnWMdJ9zSd+GeoMIxxygN4KbSTv1\nkd6v20jrGKQuiX8NISw/yvOsCPx1oBv2LaPcdyra/lCZiOVJO/n+9/expEH1Y9U/1ceN5HekcLDl\nwO1bTuC5lnT/2W+q2+nVwGDQf/1YM5rmfU5vAG//e7Eu8OKxapglU9kGprrd9Pbxm/XdtgmLWwSn\nYx6PMN9bbCAdCr0faaFf3nf70aRR+nUI4XDgscAnSIMwqwk873jJcy/gvBDCaaQPkEWkjeT0GOM1\npC6F7UgDqD5DanI9lDTgd7ym4AUjzP8CUvPtCaRmyB8M/H+Ppp4NSQPcfkPqB86B7ZtBYMeTmon3\njTHeG9KRLqeHEM6NfYcXjuJxzes4l7SDy5t5judA0oDCU0gfuM8lHd3yqREGkb46hPAH0uC5XUnv\nWX/wGlwuHwGuDyFcRTpa4gekgLsV8PkY47cnUF+/Rzx/WHyY4xYxxium8FzjuQR4SwjhJtKRH+8h\n9eNP5LGPWkdijPeHEL5EGqdzehznUNpBzSDkA4HPhnSm00tZfBjvHn3djAeSukWvCCGUpB3/xsCf\nm2+2FwN5COFY0pEQrySdLGy6jLR9DIsFADEN+r8a2LMZZ3QLqWX5j6QulhFN9XGD82+e6x/Nvq8M\nIRxC6oLenrRdjbf8lnT/2W+q2+nhwP+EEM4gdc+tz+KA3D92bfC1TNc+5+ekD/WDmpa0B5vXctMI\n85xJI81rKvOf0nYTY7w5hPADYK8Qwv2kdbEgfQkaaQDxEptvLTaPOsNk041yzOAdmyMzNiHtdE8m\nHVd/IYtbTfqfc9z5jPD8NYvP0/FF0piCh5vmYjre/8WkQ0O/RBp5fiLpsMJJz78JJueTdm6POqwv\nxnghqQ94BdJrPYc0av8a4MEQwptJh+W+vdf11IzOPwc4pWlmHsvepJX2c6Qusb37m8pHqrmZxyWk\n1qH1Sd1nbwcOjDHuM8Jr3p70Tet00gDareMjT071iHnEGP9I2mn9gnQUztdI5664j3RIdP/jJmLw\nNfTGuYx3FM9o7+F4z78HKTjtTzrK57ukFsjBx05mHe196JwyRr2jijGeTGqJfAVwNum927X/vW5a\nCDcm7fSPJYXd7Vjc5XkC6ajBNzd/r8LoR7ZNxUivfbTbxpoe6XETeZ6J1rUTKbAeQTqC8CTSNjDe\n8030ceOudzHG/yKdbmAn0ra7kLQtj7d/m7b95yS208EariG12DyTtE94OSl8wCO7jwZf87Tsc5oe\nge1Ip+w4jnQ49n6kbr3x1plBo91nKq2zU32uiW43Iz3Xm0nv36GkL/X7kd67iSyHSde6YNGiudAq\nq7kqLD4J1zZx9MMyOymkk6+9JMY42Kw9tJqWlu1jjE9vuxZpuoUQ3kpqvXlqcyCEOsiuKGnmbEpq\nkh96IZ18onfyrY+0XI40LUIIx5O6bO8A/oXUgnWGoabbDDaaDfOyWTDGOJcuhvgZUnP/F3n0yf2k\nuWpVUjfQKqRxgyeRum7VYXZFSZKkzphvg4clSVKHGWwkSVJnGGwkSVJnGGwkSVJnGGwkSVJnGGwk\nSVJnGGwkSVJnGGwkSVJnGGwkSVJnGGwkSVJnGGwkSVJnGGwkSVJnGGwkSVJnGGwkSVJnGGwkSVJn\nGGwkSVJnGGwkSVJnGGwkSVJnGGwkSVJnGGwkSVJnGGwkSVJnGGwkSVJnGGwkSVJnGGwkSVJnGGwk\nSVJnGGwkSVJnGGwkSVJnGGwkSVJnGGwkSVJnGGwkSVJnGGwkSVJnGGwkSVJnGGwkSVJnGGwkSVJn\nGGwkSVJnGGwkSVJnGGwkSVJnGGwkSVJnGGwkSVJnGGwkSVJnGGwkSVJnGGwkSVJnGGwkSVJnGGwk\nSVJnGGwkSVJnGGwkSVJnGGwkSVJnGGwkSVJnGGwkSVJnGGwkSVJnGGwkSVJnGGwkSVJnGGwkSVJn\nGGwkSVJnGGwkSVJnGGwkSVJnGGwkSVJn/H8uTMehrN7cHgAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x108aee090>"
]
}
],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Step2: Identify if problem is smooth or non-smooth.**"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\"\"\"\n",
"Smooth vs non-smooth\n",
"\"\"\"\n",
"x = np.linspace(-1.5, 1.5, 101)\n",
"\n",
"# A smooth function\n",
"pl.figure(1, figsize=(3, 2.5))\n",
"pl.clf()\n",
"\n",
"pl.plot(x, np.sqrt(.2 + x**2), linewidth=2)\n",
"pl.text(-1, 0, 'Smooth functions are continuous and easier to solve', size=15)\n",
"\n",
"pl.ylim(ymin=-.2)\n",
"pl.axis('off')\n",
"pl.tight_layout()\n",
"\n",
"# A non-smooth function\n",
"pl.figure(2, figsize=(3, 5))\n",
"pl.clf()\n",
"#pl.plot(x, np.abs(x), linewidth=2)\n",
"pl.plot(x, linewidth=2)\n",
"pl.plot(x+1, linewidth=2)\n",
"pl.text(80, 0, 'Non smooth functions can be difficult or impossible to solve', size=15)\n",
"\n",
"pl.ylim(ymin=-.2)\n",
"pl.axis('off')\n",
"pl.tight_layout()\n",
"pl.show()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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/8DDNfy1gc+/90cMx/8EI5/ULgPm9928N5291fYnUObcftrKnAHsCuwIZEFUZVwNzA0cA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\nGWPdu5wAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x108b0e050>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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kbZuVXtZGo2oX9ZvdjVmTlKjWHuwDnFQsVu1MDJIkrSgrtqw1eq2DgWOAB4GL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\n0gSzrEmSJE0wy5okSdIE+/+OAuS3hEpvFQAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x108ace9d0>"
]
}
],
"prompt_number": 3
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Step3: Identify boundries / constraints.** "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\"\"\"\n",
"Optimization with constraints\n",
"\"\"\"\n",
"x, y = np.mgrid[-2.9:5.8:.05, -2.5:5:.05]\n",
"x = x.T\n",
"y = y.T\n",
"\n",
"for i in (1, 2):\n",
" # Create 2 figure: only the second one will have the optimization\n",
" # path\n",
" pl.figure(i, figsize=(3, 2.5))\n",
" pl.clf()\n",
" pl.axes([0, 0, 1, 1])\n",
"\n",
" contours = pl.contour(np.sqrt((x - 3)**2 + (y - 2)**2),\n",
" extent=[-3, 6, -2.5, 5],\n",
" cmap=pl.cm.gnuplot)\n",
" pl.clabel(contours,\n",
" inline=1,\n",
" fmt='%1.1f',\n",
" fontsize=14)\n",
" pl.plot([-1.5, -1.5, 1.5, 1.5, -1.5],\n",
" [-1.5, 1.5, 1.5, -1.5, -1.5], 'k', linewidth=2)\n",
" pl.fill_between([ -1.5, 1.5],\n",
" [ -1.5, -1.5],\n",
" [ 1.5, 1.5],\n",
" color='.8')\n",
" pl.axvline(0, color='k')\n",
" pl.axhline(0, color='k')\n",
"\n",
" pl.text(-.9, 4.4, '$x_2$', size=20)\n",
" pl.text(5.6, -.6, '$x_1$', size=20)\n",
" pl.axis('equal')\n",
" pl.axis('off')\n",
"\n",
"# And now plot the optimization path\n",
"accumulator = list()\n",
"\n",
"def f(x):\n",
" # Store the list of function calls\n",
" accumulator.append(x)\n",
" return np.sqrt((x[0] - 3)**2 + (x[1] - 2)**2)\n",
"\n",
"\n",
"# We don't use the gradient, as with the gradient, L-BFGS is too fast,\n",
"# and finds the optimum without showing us a pretty path\n",
"def f_prime(x):\n",
" r = np.sqrt((x[0] - 3)**2 + (x[0] - 2)**2)\n",
" return np.array(((x[0] - 3)/r, (x[0] - 2)/r))\n",
"\n",
"print \"Minimum found at\", optimize.fmin_l_bfgs_b(f, np.array([0, 0]), approx_grad=1,bounds=((-1.5, 1.5), (-1.5, 1.5)))\n",
"\n",
"accumulated = np.array(accumulator)\n",
"pl.plot(accumulated[:, 0], accumulated[:, 1])\n",
"\n",
"pl.show()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Minimum found at (array([ 1.5, 1.5]), 1.5811388300841898, {'warnflag': 0, 'task': 'CONVERGENCE: NORM_OF_PROJECTED_GRADIENT_<=_PGTOL', 'grad': array([-0.94868331, -0.31622778]), 'nit': 2, 'funcalls': 3})\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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WPFeN5uJi3u2dtbUj+e4NhqbJNTl9y9D4PWYgC31uNzaxW85EoqvW6urG3pCl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\nytnt/+cLa3dbAHvKsA+7Gj1mAtbr96L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"text": [
"<matplotlib.figure.Figure at 0x108af00d0>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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WPFuN5pJ83u2dtbUg+e41hqbJNjl9x9D4XaY/C312NzaxW85EoqvW7ujG7tBK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\nAgUGGAWhL1BggFEQ+gIFBhj/DzqHBU2XQ7KFAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x108af7890>"
]
}
],
"prompt_number": 4
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Step4: Determine the size of data. Some optimizing solvers won't work on too large / too small data.**\n",
"<img src=\"http://www.nuxeo.com/wp-content/uploads/2014/07/140630_nuxeo_comic_06_big_data_blog1.jpg\">"
]
},
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Part II - Simple Optimization Problem"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Reference: http://isaacslavitt.com/2014/06/20/linear-optimization-in-python/"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Giapetto\u2019s Woodcarving, Inc., manufactures two types of wooden toys: soldiers and trains.\n",
"\n",
"- A soldier sells for 27 dollars and uses 10 dollars worth of raw materials. Each soldier that is manufactured increases Giapetto\u2019s variable labor and overhead costs by 14 dollars. \n",
"\n",
"- A train sells for 21 dollars and uses 9 dollars worth of raw materials. Each train built increases Giapetto\u2019s variable labor and overhead costs by 10 dollars. \n",
"\n",
"- The manufacture of wooden soldiers and trains requires two types of skilled labor: carpentry and finishing. A soldier requires 2 hours of finishing labor and 1 hour of carpentry labor. A train requires 1 hour of finishing labor and 1 hour of carpentry labor. \n",
"\n",
"- Each week, Giapetto can obtain all the needed raw material but only 100 finishing hours and 80 carpentry hours. Demand for trains is unlimited, but at most 40 soldiers are bought each week. Giapetto wants to maximize weekly profit (revenues-costs).\n",
"\n",
"- Formulate a mathematical model of Giapetto\u2019s situation that can be used to maximize Giapetto\u2019s weekly profit."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So here we basically have a **convex**, **smooth** problem with clear **constraints** and **small data**."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# use seaborn to change the default graphics to something nicer\n",
"# and set a nice color palette\n",
"sns.set_palette(\"Set1\", 8)\n",
"\n",
"# create the plot object\n",
"fig, ax = plt.subplots(figsize=(8, 8))\n",
"s = np.linspace(0, 100)\n",
"\n",
"# add carpentry constraint: trains + soldiers <= 80 \n",
"plt.plot(s, 80 - s, lw=3, label='carpentry')\n",
"#plt.fill_between(s, 0, 80 - s, alpha=0.1)\n",
"\n",
"# add finishing constraint: trains + 2*soldiers <= 100 \n",
"plt.plot(s, 100 - 2 * s, lw=3, label='finishing')\n",
"#plt.fill_between(s, 0, 100 - 2 * s, alpha=0.1)\n",
"\n",
"# add demains constraint: soldiers <= 40\n",
"plt.plot(40 * np.ones_like(s), s, lw=3, label='demand')\n",
"#plt.fill_betweenx(s, 0, 40, alpha=0.1)\n",
"\n",
"# add non-negativity constraints\n",
"plt.plot(np.zeros_like(s), s, lw=3, label='t non-negative')\n",
"plt.plot(s, np.zeros_like(s), lw=3, label='s non-negative')\n",
"\n",
"# highlight the feasible region\n",
"path = Path([\n",
" (0., 0.),\n",
" (0., 80.),\n",
" (20., 60.),\n",
" (40., 20.),\n",
" (40., 0.),\n",
" (0., 0.),\n",
"])\n",
"patch = PathPatch(path, label='feasible region', alpha=0.5)\n",
"ax.add_patch(patch)\n",
"\n",
"# labels and stuff\n",
"plt.xlabel('soldiers', fontsize=16)\n",
"plt.ylabel('trains', fontsize=16)\n",
"plt.xlim(-0.5, 100)\n",
"plt.ylim(-0.5, 100)\n",
"plt.legend(fontsize=14)\n",
"plt.show()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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Stm3bYqdXKXdOEQKAK6RGrpKAH+APXAC6AovT1lkMdHfI6OxA1w0QEUfq06cf\nPj4+DBkygK5dwzlz5ky263l4eFxXn6cuu3b/+edfoVGjO3nppWcYPXooALNnz8PHxyfTc7Lbdm6y\n7ie78fTt259Ro8azevWnPProw4wfP4rvvtvKLbek/n319/dn5sz3OHXqJMOGPcqSJR8yfPgYAIoX\nTz1zoVu3nvTvP5APP/yACRNGExt7ib59+5OxCejSpQfVqlVnzJjhdOnSlsjIfTmOu127jhw+/Ae1\na9ehatVqmR4bP34SvXo9xMKF84mIeIgnnhjP/v17qFAhb/MPbMXjRsd1CophGB2AtcBVYKZpms8Y\nhnHeNM3AtMc9gL/T72cnJiY2Jen92azbdYtlWY95Pew88psXl5DEY4t3cSkuNVGOuq9GoZobEBQU\nQExMrKOH4ZIGbe9juT2/+fJc1pT80L9h+3PG1/j777fy7LNP8NVXm/H3L+bo4eRbUFCAFbMVsucU\ncwIMwwgC3gPqAueBlYZhdM64jmmaKYZh5JpYAgP9uXjIBK6FgFIXz1Ckpn1mzdpC/7AQ3t34PwA+\n3R3Ng81DKOLtLAXNjQUFBTh6CC5Pr7F96fW1P0e/xqtXr6Zy5cqULl2azZs389FHH9G5c2eqVg2+\n8ZNdnFOEAOAuYIdpmocADMNYCYQBZwzDCDZN87RhGBWAs7lt5Pz5yyRHDIKZhy3LzvbsRZF5i/Co\nHmLH4d+8liGBLCnqzaW4RE5fiOO/3x+mfb3C8Q/TGRO+K9JrbD/6N2x/zvAaHz9+knfemclff52j\nTJmyNGvWnOHDxzh8XLaSn5DlLCHge+CdtAmC/wIdgHdIPSATAbyR9t81N9qQ5+31ST2RIM25cyQM\nHuC0QSDrmQIrd0XT+tZyOlNARMRG+vbtn3aMX7Jyinca0zQvAVOA1cB2YC+wBXgFaGYYxj6gSdo6\neZcWBFL+PGKbAduYzhQQERFHcJYmANM0FwGLsiyOJb9nBHh7Q2KiUzcCum6AiIg4gsu/y3h07Jwa\nBMCpGwG1ASIiUtBcPwRUuKVQBAFdN0BERAqay4cAKDxBQG2AiIgUJLcIAVA4goDaABERKUhuEwKg\ncAQBtQEiIoXLqVMnCQsLxTQPOnooeeZWIQCcPwioDRARcV6jRg1h+vQ3My0rXz6Ydeu+sXxLYGHi\ndiEA0oNAF6cNAmoDREQKD09PTwIDS+Pl5eXooeSZW4YAAI8KFZw2CKgNEBF727dvD6+88hzdurWn\nfft7GTxXaL9vAAAgAElEQVQ4giNHDue4/gMPdOHjjxcza9bb9OjRkfvv78SyZUszrXP+/N+8+OIz\ndOvWjm7d2vHyy89x/vx5y+MLFsylf/8H+fHH7Qwc+Ajt29/LU089zsWLF3Ida/qn76VLF/Lgg93p\n0iWc2bPfyfQVx4mJiSxaNJ+HH36Atm1bMHhwf37+eUem7ezevYtHH+1Lhw6tePLJCfz443bCwkI5\nffo0AJcuXeSFF57m/vs70br1PfTr15svv/zc8vxXX32RvXt3s2rVSsLCQi3PzXg4IDk5mfvv78Rn\nn32Sad/Hjx8jLCyUP/4wAYiLi2PmzGk8+GB32rVryahRQzh48PdcXwd7cJqLBTmCR4UK0LELKV9+\n7nQXFOp4ezCf/RrNpbhESxtQmL5hUMRd+e2Zhf/O/+CZ8E+B7TO5SHEu3/kkVxqOtmr9xMREJk8e\nT8uW9zF16kx8fX353/8O3vCT7PLlS+nYsQv/+c/bbN68kffem0n9+g2pV+92kpOTmTBhFEWL+vHm\nm6lv0NOnv8ngwYN5772Flm2cPn2aTz5ZxpAhI4iLu8KMGVP54IM5TJr0dK773rTpG5o3b8kLL0wh\nMnIfs2ZNxzDq0KZNOwCmT3+TAwciiYgYREhIDTZv3sikSWNZsOAjatasxenTp5k4cTQ9evSie/ee\nHD78B9Onv5Xpa4nj4+OpU6cu/fo9iqenJ999t4XXX3+Z8uWDueOOUMaNe5yoqONUrVqdoUNHAlCy\nZCnOnDlt2Yanpydt2rRjw4av6dnzQcvyjRu/plq16tSqZQDw9NOTSExMYOTIcZQrV55161Yxduww\nli37jDJlylr1/9EW3LYJSOesjYDaAJHCyW/vuwUaAAA8E/7Bb++7Vq+fkJBAQkI8997bmlq1alOl\nSlXatGlH1arVcn1epUpVGDFiLIZRh6FDR1KsWDF+/fUXAHbt+plDh/5gxIgxGEYd6tS5lWHDRhEZ\nGcmuXb9YtnHlymUmTHiCpk3v5t57W9Oixb2ZHs+Jj48vTz31PHXr1qN3775Uq1bd8rwzZ06zfv1a\nJk58ivDw9tSsWYshQ0ZQs2Zt1q5dBcCaNZ/i4+PLqFHjqFy5Cvfe25rQ0CaZ2oSyZYPo0+cRatas\nRUhIDQYMGETDho3ZtOkbAIoVK463dxGKFi1KYGBpAgNL4+l5/dtoeHgHDhyIJDo6yrJs48avCQ/v\nCKS2MLt37+Tpp1+kRYt7qVPnViZMeIKiRf345psvb/ha2JJbNwHpnLURUBsgUvhcaTDKIU3AlQaj\nrF7fz8+PXr368PzzT9Ko0R3ccUco997bmvLlc/4GUw8PD+66q6nlvqenJzVq1LLU/UePHqVYsWLc\ndtvtlnVuv70BxYoV4+jRI9xxRygAwcEVqFKlqmWd2rUNyxvf3r27efzxsZbHJk9+mrZt2wMQGtok\n03hq167D+fN/A3DkyCGSk5MZP35kpnUSEuIpVSoQgGPHjtKgQcNMn/wbNw5l3brVlvtJSUl89NEi\nNm/eyLlzMcTHJ5CYmECRIj45vi7ZSQ0RNdm48WsGDBjEb79FcvJkNOHhqb/LoUN/kJSURL9+va8b\n78mT0XnaV34pBKRxxiCg7xQQKXyuNBxtdS3vSMOGjaJ79wf49ttv2L79Oz74YA6zZ8+jTp26OT7H\n398/031PT09SUqxpKK+98fr5+WXZhhfJyamfxuvUqcuiRcssjwUGlk59todHDvtOfV5SUjIeHh4s\nWLAEL6/Mb2u+vkUttzN86LdsN6Ply5eycOE8nnjiWWrVMvDz82PmzGlcvnzZit8xs3btOrB+/VoG\nDBjExo1fUb9+Q0vISk5OIjCwNHPmzL/uecWKFc/zvvJD7yYZOOOhAZ0pICL2EhwczMMPRzBr1lxq\n167D+vXrbnpb1apV499//yUycp9l2b59e/j333+pbuUHKV9fXypWrGT5yfrGn1X6m3r6qXnnzp3L\n9PyKFStRtmzZtPFVZ9++3SQnXwstu3b9nGl7+/btpWnTu+nQoTM1a9aiXLny7N27J1NYKFKkCImJ\nSTf8Xdq0aUd0dBS//RbJ5s2baNeuo+WxmjVrc/7833h4eFw33lKlSt1w27akEJCFswUBzQ0QEVs7\ndeok7703i8jIfURHR/Hdd1s5fPgQ5cqVy9N2UlJSLJ/GQ0ObUqtWbd57bxYHD/7OwYMHeP/9d7n9\n9ttp3PjOfI03436yExxcgW7devLaay+xdeu3REdHcfDgAZYtW8q2bVsA6NatJ/Hx8cyZM5Pjx4+y\nbdtmdu78GQ8PD9Lf46tUqcrevXv44YftHD36J++8Mw0vL89M+w4OrsCBA5EcOXKICxcu5DiucuXK\n07BhY9566zX+/fcf7ruvjeWxhg0b06RJM556aiI7dvzAyZPRREbuY8GCuezduydfr1VeKQRkw9mC\nQNY24NvfzzpkHCLiGooWLUpU1HGee+5JBgzow2effUJExEAefjgiT9tJfQO99il52rR3KV8+mMmT\nxzF58ngqVarMvHnzclw/4/K87Ofasmv3x4+fRK9eD7Fw4XwiIh7iiSfGs3//HipUqACkth7Tps3i\n119/YejQgXzxxTqGDRtFSkoKAQEBAEREPEbHjl2YOvV1nnxyIuXLl6dNm3aZ9t2nTz98fHwYMmQA\nXbuGc+bMmRx/h/DwDhw+/AfNmt1D8eKZa/4pU97knntaMGvW2/Tr15vnn3+KEyeOExQUlOtrYWse\nuaWrwiYmJjYFYPXgaxM9ujS++UkWKadOkvLl+tQ5AgBlyzpsjsCqX6MtcwPKBfjy/iONHD43ICgo\ngJiYWIeOwVUN2t7Hcnt+8+UOHIlr079h+3Pm13jFiuUsWfIh69dvdPRQ8iUoKCD3FJULNQG5cKZL\nDGtugIhI/nz22QpLlb9gwVwWL55P9+49HT0sh1IIuAFnCQKaGyAikj8nT0bxzDOTGTQogo0bv6FH\nj14MGDDI0cNyKJ0iaAWPCrdAx87XDg046PRBXTdAROTmjR49gdGjJzh6GE5FTYCVnKERUBsgIiK2\npBCQB84QBDQ3QEREbEUhII8cHQTUBoiIiK0oBNwERwcBtQEiImILCgE3yZFBQG2AiIjYgs4OyAdH\nnjWgMwVEnFNSUhIXL14o0H2WLFkKLy+vAt2nuAaFgHxyVBDQNwyKOKeLFy/w15x3KZnl2/Lstr8r\nV2DEKEqXLpOn5yUnJzN16uts3bqZ2NhLzJo1l4YNG9tplNeEhYUyZcobtGzZilOnTtK7dzfmz1+K\nYdTJdn1r1nG0jL9TYaMQYAOOCgJqA0ScU0k/P0rf4BvwHO3HH/+Pzz9fw9SpM6ld2yAgoESB7Hfd\num8oXjygQPZVUArz76SPjTbiiDkCmhsgIjcrOvoEQUHlaNKkGYGBpfH2LpjPhIGBpSlSpEiB7Cs3\nienfCWMDzvI73QyFABtyRBDQmQIiklevvvois2ZNJybmLGFhofTq1c3y2Jo1nxIR0Ye2bVsQEfEQ\nGzZ8lem57703i759e9K69T306tWVOXNmEh8fb3n8zJnTzJjxFo880os2bZrToUMHvv12g+XxsLBQ\ntm3bnGmb587FMHHiGDp0aMVjj/Vj//69uY7/9OlTPPPMJLp1a0eXLuG8+OIz/P33Xzmuf+rUScLC\nQvnxx+08+eQEOnZszbp1qV80t3Xrtzz2WD/Cw1vSp8/9rFixLNPXA585c5oJE0bTvv19DBs2kP37\n99K2bRhffbU+x98pOjqKyZPH0alTa3r27Mzbb79BXFxcptd/8uTxrF+/lkce6U3Hjq157bWXuHr1\n2joFRYcDbKygDw1oboCI5NW4cY8THFyBL75Yx4IFS/H0TP17sXTpItatW0VExEDq1r2dn376kddf\nf5mAgACaNWsOgJ+fH08//QKBgaXZvXsnc+fOwcfHh0GDhgEwbdobXLhwnkmTnqFcuXJcvHiWixev\n5DqeGTPeYsSIMYwdO5HPPvuE8eNH8t//rqZs2eu/Vveff/5hyJAB3HNPC1555Q2uXo1jyZKFPPnk\nRObOXZjr1xLPmDGVESPGMG7cJLy8vNi06RvefvtNBg4cTOPGoezbt5sPPngPLy9vevbsTXJyMhMn\njqFMmbK8++4HxMXFMXv2dBISEnLcx5UrVxg5cjB169Zj1qwPuHTpIm+8MYUpU55nypQ3LetFRu7D\n29ubSZNSv0L4nXemUblyVfr1G5Dra2Vreqewg4JuBNQGiEheFCtWHD8/f7y8vAgMLE3JkqVISEhg\nyZIFDB06ks6duxMSUoM+fR7hnnvCWLVqpeW5AwYMol69+lSsWInOnbvTvXtPNm36xvL45cv/0rBh\nYxo0aEiFCrcQFhZGkybNch1PkybNuO++NlSpUpXRoyfg4eHJ6tWfZrvuZ599QokSJZg8+Wnq129I\naGhTxo+fxO+//8bBgwdy3U+zZs1p2bIVwcEVCAoqx/z579OnTz8eeOAhQkJq0L37A3Ts2MWy719+\n+Yljx/5k+PDR1KxZi3r1bqdnzwdJSkrKcR8bN37NX3+dY8KEyYSE1KBhw8b07z+Qbdu2EB0dZVkv\nLi6OZ599iQYNGtG5czcaNWrMrl0/5zp+e1ATYCcF2QioDRCR/IqKOkFcXBxvvDGFN9541bI8KSmR\nChVusdzfsmUTK1Ys5+TJKC5fvkJyclKm+rxXr4d4/fWX2bdvD3fcEUq3bp0oV65Krvu+8867LLe9\nvb1p2LARR49m/6Hp0KE/iIo6QXh4y0zLPTw8OHkymltvvS3H/dx1V1PL7StXrhAdHcXixfNZsuTD\nDL/vtTf4Y8eOUqxYsUxnJTRufGeubcOxY39SrVr1TC1GaGjqfo8e/ZOKFSsBcNtt9fDPMHm0Vi2D\n7du/y3G79qIQYEcFGQSyninw7e9naV8v2Kb7EBHXlZycOqn4jTemU7585r8d6ZMGIyP38/zzT9Gn\nzyOMHfs4AQEBbNr0DfPnv29Zt2XLVoSGNmHz5o38/PNPPPTQQ4wcOZaePR+0eiwpKSk5vtGmpCRz\n991hjBw59rrHAgNL57rdMmXKWm4nJ6e+2U+a9DT16tXP5VmZx5FbALg2xixb8Eh9Xsbn+vllPnvE\n09OTlJSCn9itj4p2VlCHBrKeKbByV7TOFBARq1WuXAVfX19Onz5FxYqVMv2kh4L9+/dSvHgAw4eP\noU6dW6lYsRKRkfuue2P09y9G587defnl1xk4cGCO1X66nTuv1eCJiYns3bubqlWrZ7tuzZq1OXLk\nMOXLB183Tv88nJZZrFhxKlS4haioE9dtJ/3TerVq1fn3338wzYOW5+3a9Uum5iOratVCOHbsT2Ji\nzlqW/fTTj6SkpFC1ajWrx1dQ1AQUgIJqBHTdABHncPFK7hPhbL2vvF0mKHs+Pj4MHDiE2bNnkJKS\nQoMGjbhy5TK//bYfT08vunbtQZUqVfnnn1hWrvwvTZveza5dv/C//x3M9KY4Y8ZUmjW7h0qVKnPm\nzGm+++47goLK5brvn3/ewdat3xISUoNVq1aSkpJCjx4PZLvuAw88xJo1n/HCC0/x8MMRlCxZipMn\no9myZROjRo3PUxAYOnQUr732IgEBATRtejeJiYmY5kHOnTtHv34DCA1tQrVq1Xn//VmMGjWeuLg4\nVq/+FC8vrxwbgfDw9nz44Qe8/fabDB48jEuXLrFkyUJatmxlCRfORCGggBREENDcABHHK1myFIwY\nVWD7K5O+zzxKfRPL/EbWt29/AgNL89lnK5gxYyq+vr7Urm3Qt29/AO65J4xRo8bx1Vef8/HHi7nr\nrqYMHz6G1157KcNWUpg+/S3OnTtLlSpVCQtrTteuvXIdx5gxE1m1agUHDvxGxYqVePvtdzMdU8/4\nhlu8eHHmzVvM++/P4rnnnuTixQuUK1eeu+5qho+Pzw1+38xat26Lv78/S5Z8yIcfzsPDw4OQkBrc\nf39vy3OmTZvFG2+8yqhRg6lSpRojR45l3LgROV4cyNe3KLNnz2PGjKmMGjWUokWLEhbWkhEjxmQa\nS9bhZD1cUFA8cqs1CpuYmNgUgNWDV1uWdWkc7bDxZCfl1MlrQQCgbFmbBoG4hCQeW7yLS3Gp2x91\nXw27tQFBQQHExMTaZdvubtD2Ppbb85svd+BIXJv+Ddufq73Gf/zxPwYOfJglSz6hup2/I8ZaQUEB\nN50e9BGxgNl7joCuIigiYjvffbeVn3/eQVTUCVav/pSXXnqG+vUbOk0AyC+FAAewdxDQdQNERGzj\n8uV/mT79TSIiHmLx4gXUrl0n00V/CjvNCXAQe84R0NwAERHbaN++E+3bd3L0MOxG7woOZM9GQG2A\niIjciEKAg9krCGhugIiI3IhCgBOwVxBQGyAiIrlRCHAS9ggCagNERCQ3CgFOxB5BQG2AiIjkRCHA\nydg6CKgNEBGRnCgEOCFbBwG1ASIikh2FACdlyyCgNkBERLKjEODEbBkE1AaIiEhWCgFOLtsgMCgi\nz0FAbYCIiGSlEFAIXBcE/vrrpoJA1jbg29/P2nqoIiJSiCgEFBK2CALXtQG71AaIiLgzhYBCxBZB\nIGMbEBMbrzZARMSNKQQUMvkNAmoDREQknUJAIZTfIKA2QEREQCGg0MpPEFAbICIioBBQqOUnCKgN\nEBERhYBC7maDgNoAERFRCHAB2QYBK64sqDZARMS9KQS4iJu5xLDaABER96YQ4EJuJgioDRARcV8K\nAS4mr0FAbYCIiPtSCHBBeQ0CagNERNyTQoCLyksQUBsgIuKeFAJcWF6CgNoAERH3oxDg4qwNAmoD\nRETcj0KAG7A2CKgNEBFxLwoBbsKaIKA2QETEvSgEuBFrgoDaABER96EQ4GZuFASytgErd0WrDRAR\ncVEKAW7oRkGg4+3BlPRLfexs7FU2H4xx1FBFRMSOFALcVG5BoGgRL+5vlGFuwE7NDRARcUUKAW4s\ntyCQcW6A2gAREdekEODmcgoCvlHHMp8poDZARMTlKARIjkGgQ8AVtQEiIi5MIUCA7IOA1/CB3F/N\nz7KO2gAREdeiECAW2QWBtm+No4SPB6A2QETE1SgESCZZg0DRM6fo9usXlsfVBoiIuA6FALlO1iDQ\nfud6Slz9B1AbICLiShQCJFsZg0DRxHi67fnK8pjaABER1+Dt6AGkMwyjGDAHqA/4Ao8CB4ClQAhw\nGOhnmuY/Dhukm/GocAt07EzKl+tp//sW1tZvzyW/AEsb8EhwSUcPUURE8sGZmoA5wDbTNBuRGgQO\nAs8BP5imWR/YATzrwPG5pfRGoCjJdNv3tWX5ih1/kpCoNkBEpDBzihBgGEZJIMw0zQ8BTNNMNE3z\nItAVWJy22mKgu4OG6NbSg0D7P76nxJVYAM5eSWbdxj0OHpmIiOSHU4QAoDoQYxjGIsMwIg3DmGcY\nhj9Q3jTNM2nrnAHKO26I7s2jwi34hYfTLXKDZdmizf8j/vBhB45KRETyw1nmBHgDocAUYDgwF+iV\ncQXTNFMMw0jJbSOBgf54e3tlWlasmK9tR+rOalanR9FTrI2L5VLRAGL8A9n0+nv0nTaJIjVrOnp0\nLisoKMDRQ3Bpen3tT6+x83KWEBAF/GWa5ucAhmEsB/oDpw3DCDZN87RhGBWAs7lt5Pz5y9ct+/ff\nq3YYrvvyCCxN94snWEJdAD6t0YKWDzyE/wcL8Kge4uDRuaaYmFhHD8FlBQUF6PW1M73G9pefkOUU\nhwNM0zwNHDIMo4lhGJ5AJ+Bb4HMgIm21CGCNg4YoGXQoEU+J5NRwFRNQlq2la1u+fVBERAoPpwgB\naSKAd4D/ARWB5cArQDPDMPYBTUg9XCAOVtQjme5e1y4Y9FnDTiT8fV5BQESkkHGWwwGYpvk/oGk2\nD+mMACfUweMcawnmYop3ahtQ627amt+TMHgAReYt0qEBEZFCwJmaAClEinok08vnnOX+Z406k+Dp\nZfkaYjUCIiLOTyFAbloXn78pQQIAMcXLsLXuvakPKAiIiBQKCgFy0/w8UujuccZyf1XLPiQUK556\nR0FARMTpKQRIvnTwOGdpA85ehe+fnQV+fqkPKgiIiDg1hQDJl6IeyZnagJVnvUmZ9b6CgIhIIaAQ\nIPmWqQ2IvcpWvyp4z56rICAi4uQUAiTfsrYBK3ZGkdSgsYKAiIiTUwgQm8jaBmw+GINn4zsVBERE\nnJhCgNhEdm1AQlKygoCIiBNTCBCbya4NABQERESclEKA2ExObQAoCIiIOCOFALGpnNoAUBAQEXE2\nCgFiU7m1AaAgICLiTBQCxOZyawNAQUBExFkoBIjN3agNAAUBERFnoBAgdnGjNgAUBEREHE0hQOwi\naxvwyc4T17UBkBYE5nygICAi4gAKAWI3GduAmNh4vv39bLbreTa6Q42AiIgDKASI3Vw3N2DX9XMD\n0unQgIhIwVMIELuytg0ABQERkYKWrxBgGEZJWw1EXFNe2gBQEBARKUhWhQDDMIYYhjEpw/16hmF8\nD5w3DGOXYRjBdhuhFHp5aQNAQUBEpKBY2wSMAuIy3J8OBAMvAxWBV2w8LnEheW0DQEFARKQgWBsC\nqgK/AxiGUQpoCYwzTfNFYArQzi6jE5eR1zYAFAREROzN2hDgCZRIu9087b9b0v57AChny0GJ67mZ\nNgAUBERE7MnaEHAI6GYYhg/wMPCDaZqX0x4LAv62x+DEtdxMGwAKAiIi9mJtCHgL6AdcBHoDMzM8\ndh+wz8bjEhd0s20AKAiIiNiDVSHANM1lQAtgMlDDNM1VGR4+S+ZQIJKjm20DQEFARMTWrL5OgGma\n203TnGWa5tEsy583TfNLm49MXFJ+2gBQEBARsSXvvKycdj2AKkDRrI+ZpvmdrQYlrq2DxznWpJTn\nEkUsbUD7etZfaiI9CCSOHApXrliCQJF5i/CoHmLHkYuIuBZrLxZU0TCMLcBJYAewNcvPlhyeKnKd\n/LYBoEZARMQWrD0c8B7QkNRj/z2BVll+WttldOKy8jM3IJ2CgIhI/lh7OKA5MNM0zRfsORhxH+lt\nwJKUSkBqG9D61nIU8crb11lke2hgUARF5i/WoQERkRuw9i/uSeBHew5E3I8t2gDIphH46y81AiIi\nVrA2BCwGHrHnQMT92GJuQDrPxnfiPecDHRoQEckDaw8H/A3cYRjGYWAVad8jkJFpmh/acmDiHvJ7\npkBGno3u0FkDIiJ5YG0TMA8wgOrARGB+Nj8ieWbLNgA0WVBEJC+sDQEhVvyI3BRbzQ1IpyAgImId\nqw4HZL1KoIgt2epMgYx0QSERkRu7+b+yIjZk6zYA1AiIiNxIjk2AYRh/At1N09ybdjsF8MiyWvqy\nFNM09fFKbpo92gBQIyAikpvc/sJuA2Iz3P4u7b8ZfzIuE8kXe7QBoEZARCQnOTYBpmkOyO62iL3Y\nqw0ANQIiItnRnABxKvZqA0CNgIhIVnn9KuFbgVpAqayPmaa5xFaDEveVtQ1YuSvaZm0AqBEQEcnI\n2q8SLmUYxjfAb8AaYFE2PyI2kbENOBt7lc0HY2y6fTUCIiKprP149RqpVwzsk3b/flK/PvgjYD9Q\n1/ZDE3d13VUEd+bvKoLZURAQEbE+BLQDPgA+S7sfZZrmFtM0+5P67YJj7TE4cV/2bgNAQUBExNoQ\nUAHYYZpmIhAHBGZ4bC0QbuuBiXsriDYAFARExL1ZGwJOAyXSbh8HwjI81oTMoUDEJgqiDQAFARFx\nX9aGgP8j9c0eYAnwrGEYGw3D+BR4EvjGHoMT91ZQbQAoCIiIe7I2BLwEfJl2eyowndTJgK2AVcAo\n2w9NpODaAFAQEBH3Y+23CB4CDqXdjgcmpv2I2NV1VxHcGUWrOkE2u25AVrqOgIi4kxv+JTUMw9cw\njL8Nw+haEAMSyaog2wBQIyAi7uOGIcA0zatADKlnBYgUuIKcG5BOQUBE3IG1nepXwAP2HIhIbgq6\nDQAFARFxfdZ+d8DXwLuGYXwGrAZOASkZVzBNc7ONxyZiUdBzA9JpjoCIuDJr/4J+CYQAPUg9RXAj\nsCnDz0a7jE4kA0e0AaBGQERcl7Uh4D5STwfM7UfErhwxNyCdgoCIuCJrQ8Ai4Lxpmluz/gB/AQvt\nNUCRjBzVBoCCgIi4HmtDQFXAN4fHiqU9LmJ3jmwDQEFARFyLLWZVtQDO2mA7IlZxZBsACgIi4jpy\nPDvAMIzxwIQMiz43DCM+y2p+QGlSDxeIFAhHnSmQkc4aEBFXkNtfzT+Bb9N+AH7JcD/9ZzkwDBhu\nxzGKXMfRbQCoERCRwi/HJsA0zTXAGgDDMABeNk1Tf93EKThDGwBqBESkcLPqL6ZpmgMUAMTZOEMb\nAGoERKTwKtiPTSI25OgzBTJSEBCRwkghQAo1Z2kDQEFARAofhQAp1JypDQAFAREpXBQCpNBzpjYA\nFAREpPBQCJBCL2sb8MnOEw5tA0BBQEQKB4UAcQkZ24CY2HiHtwGgICAizk8hQFyCs80NSKcgICLO\nTCFAXIazzQ1IpyAgIs5KIUBchrO2AaAgICLOSSFAXIqztgGgICAizkchQFyKM7cBoCAgIs5FIUBc\njjO3AaAgICLOQyFAXI6ztwGgICAizkEhQFySs7cBoCAgIo7nVCHAMAwvwzB2G4bxedr9AMMw1hiG\nsc8wjNWGYRR39BilcCgMbQDkHARERAqCU4UAYCxwAEhJu/8c8INpmvWBHcCzjhqYFD6FoQ2A7IOA\niEhBcJoQYBhGJaAjMB/wSFvcFVicdnsx0N0BQ5NCqrC0AZBNEBARKQBOEwKA6cAkIONf6fKmaab/\nFT8DlC/wUUmhVljaAMg5CGiOgIjYi7ejBwBgGEZn4KxpmrsNw7g3u3VM00wxDCMlu8fSBQb64+3t\nlWlZsWK+NhunXM/ZX99iQO+rfzH/ajAAn+6O5sHmIRTxdqb8m0G7+7j68VI4+YplUdLQgZRd+QlF\natZ04MBcV1BQgKOH4PL0GjsvpwgBwN1AV8MwOgJFgRKGYSwFzhiGEWya5mnDMCoAZ3PbyPnzl69b\n9vEWFj0AABRUSURBVO+/V+0xXiE1ABSG17d1ymlWUIZLFOH0hTg+2X6Edrc5cakUUhdOXrubfPYs\nZ3v2osi8RXhUD3HcuFxQUFAAMTGxjh6GS9NrbH/5CVlO8XHINM2nTdOsbJpmdeAhYLNpmv2AdUBE\n2moRwBpHjVEKr8I0NyBHOn1QROzAKUJANtJr/1eAZoZh7AOaAFMcNyQpzArT3IDr6DoCImInznI4\nwMI0zW3AtrTbseiMALGB9DZgSUolILUNaFUniCJezpqDr/GePZfEkUPhyhVLENChARGxBef/Cyhi\nI4W1DdCVBUXEXhQCxG0U5rkBCgIiYg8KAeJWCmsbAAoCImJ7CgHiVgpzGwAKAiJiWwoB4nYKcxsA\nCgIiYjsKAeJ2CnsbAAoCImIbCgHilgp7GwAKAiKSfwoB4pZcoQ0ABQERyR+FAHFbrtAGgIKAiNw8\nhQBxW67SBoCCgIjcHIUAcWuu0gaAgoCI5J1CgLg1V2oDQEFARPJGIUDcniu1AaAgICLWUwgQt+dq\nbQAoCIiIdRQCRHC9NgAUBETkxhQCRHDNNgAUBEQkdwoBImlcsQ0ABQERyZlCgEiarG3AJztPuEQb\nAAoCIpI9hQCRDDK2ATGx8Xz7+1kHj8h2FAREJCuFAJEMrpsbsMs15gakUxAQkYwUAkSycOU2ABQE\nROQahQCRLFy9DQAFARFJpRAgkg1XbwNAQUBEFAJEsuUObQAoCIi4O4UAkRy4QxsACgIi7kwhQCQH\n7tIGgIKAiLtSCBDJhbu0AaAgIOKOFAJEcuFObQAoCIi4G4UAkRtwpzYAFARE3IlCgMgNuFsbAAoC\nIu5CIUDECu7WBoCCgIg7UAgQsYI7tgGgICDi6hQCRKzkjm0AKAiIuDKFABEruWsbAAoCIq5KIUAk\nD9y1DYAcgsCgCAUBkUJMIUAkD9y5DYBsgsBffykIiBRiCgEieeTObQAoCIi4EoUAkTxy9zYAFARE\nXIVCgMhNcPc2ABQERFyBQoDITVAbkEpBQKRwUwgQuUlqA1IpCIgUXgoBIjdJbcA1CgIihZNCgEg+\nqA24RkFApPBRCBDJB7UBmWUbBHRlQRGnpRAgkk9qAzLTJYZFCg+FAJF8UhtwPQUBkcJBIUDEBrK2\nAZsPxjh4RI6nICDi/BQCRGzgujZgp9oAUBAQcXYKASI2krENOBt7VW1AGgUBEeelECBiI2oDcqYg\nIOKcFAJEbEhtQM4UBEScj0KAiA2pDcidgoCIc1EIELExtQG5UxAQcR4KASI2pjbgxhQERJyDQoCI\nHWRtA9z9KoLZURAQcTyFABE7yNoGrNwVrTYgGwoCIo6lECBiJ5obYB0FARHHUQgQsRPNDbCegoCI\nYygEiNiR2gDrKQiIFDyFABE7UhuQNwoCIgVLIUDEztQG5I2CgEjBUQgQsTO1AXmnICBSMBQCRAqA\n2oC8UxAQsT+FAJECoDbg5ng2vhPvOR8oCIjYyf+3d+9Bdtb1HcffIYnBhICoMdxShaLfIgM2XKRo\nQbFDUbHIgAx2ikbxgq2XSlunFYF2RtpKpxfaOtiRikFowWYYAa1FK4qgyC1yq8LXCYoDKWEThppA\nEAJs/3jOhrMnezab3XP2ub1fMzvZfc5zTn77m509n/08v+d5DAHSLLENmJ6dlh9qIyANiSFAmiW2\nAdPnoQFpOAwB0iyyDZg+g4A0eIYAaRbZBsyMQUAaLEOANMtsA2bGICANjiFAmmW2ATNnEJAGwxAg\nlcA2YOYMAtLMGQKkEtgGDIZBQJoZQ4BUkt424Lp7R0oeUT0ZBKTpMwRIJeltA1atXmsbME0GAWl6\nDAFSiVwbMDgGAWnHGQKkErk2YLAMAtKOMQRIJbMNGCyDgDR1hgCpZBO1AZoZg4A0NYYAqQJ62wDN\nnEFA2j5DgFQBvW2ABsMgIE1uXtkDAIiIZcCXgJcB64GVmbkyIhYDlwL7AfcD78rMx8sbqTQ8b5mz\ngatGl7KR+WUPpVHGgsAzHz4DnnxyaxCYf9FKWPKasocnlaoqTcAW4MzMPBB4B/CZiDgAOAe4KTMP\nBm4Gzi5xjNJQ2QYMT79GYMuaNeUOTCpZJUJAZq7LzDs7n28AbgP2Bk4ALunsdglwYjkjlGZH99oA\nDdZEQWDDKad6aECtVokQ0C0i9gcOpPjLf2lmjv1p9AiwtLSBSbNgojbA6wYMTm8QeG5kxDUCarVK\nrAkYExG7AFdQHBp4PCK2PpaZoxExOtnzd999IfPmzR23bdGiBcMYqjqc38E7eXQj3+j6+taHNnLi\nYctKG0/jHHcMT/3bpTx62rsZ3bwZNmzg2TNO56Wrvsz8/fcve3SNtGTJ4rKHoD4qEwIiYj5wJXBZ\nZl7d2fxIROyRmesiYk9g0jusPPbY5m22PfGEp1sNy6JFC5zfWXDx9ffz2n12Zf7cyhV39bXfq5n7\n2X/h2Y98iNHNm3luZISRk09h/kUrmbPvfmWPrlGWLFnM+vWbyh5Go80kZFXit0pEzAG+APwoMy/o\neugaYEXn8xXAVbM9NqlsXkVwOHY65DBectmXPH1QrVaJEAC8HjgNeFNE3NH5eDPwaeDIiLgbOAI4\nr8xBSmXxngLDseCII7yOgFqtEocDMvN79A8knhGg1htrA4470LWxgzbZdQQ8NKCmq0oTIGk7bAOG\nxysLqq0MAVLF7bpzUdiNbHqK6+6ddG2sZsAgoDYyBEgVd/Ihe2/9fNXqtbYBQ2QQUNsYAqSKe+tB\ne4xrAzxTYLgMAmoTQ4BUcTvPnzuuDXBtwPAZBNQWhgCpBmwDZp9BQG1gCJBqwDagHAYBNZ0hQKoJ\n24ByGATUZIYAqSZsA8pjEFBTGQKkGrENKI9BQE1kCJBqxDagXAYBNY0hQKoZ24ByGQTUJIYAqWZs\nA8pnEFBTGAKkGrINKJ9BQE1gCJBqyDagGgwCqjtDgFRTtgHVYBBQnRkCpJqyDagOg4DqyhAg1Zht\nQHUYBFRHhgCpxmwDqsUgoLoxBEg119sGXHfvSMkjaredDjmMeRd+3iCgWjAESDW3TRuw2jagbDst\nP9RGQLVgCJAaoLsNWL/paduACvDQgOrAECA1gG1ANRkEVHWGAKkhbAOqySCgKjMESA1hG1BdBgFV\nlSFAahDbgOoyCKiKDAFSg9gGVJtBQFVjCJAaxjag2gwCqhJDgNQwtgHVZxBQVRgCpAayDag+g4Cq\nwBAgNZBtQD0YBFQ2Q4DUULYB9WAQUJkMAVJD2QbUh0FAZTEESA1mG1AfBgGVwRAgNZhtQL0YBDTb\nDAFSw9kG1ItBQLPJECA1nG1A/RgENFsMAVIL9LYB37INqDyDgGaDIUBqgd42YJVtQC0YBDRshgCp\nJVwbUE8GAQ2TIUBqCdcG1JdBQMNiCJBaxDagvgwCGgZDgNQitgH1ZhDQoBkCpJaxDag3g4AGyRAg\ntYxtQP0ZBDQohgCphWwD6s8goEEwBEgtZBvQDAYBzZQhQGqp3jbg2/etL3lEmg6DgGbCECC11DZt\nwO22AXVlENB0GQKkFutuA0Y2PWUbUGMGAU2HIUBqMduAZjEIaEcZAqSWsw1oFoOAdoQhQGo524Dm\nMQhoqgwBkmwDGsggoKkwBEiyDWgog4C2xxAgCdi2DfAqgs1gENBkDAGSgG3bgFWr19oGNIRBQP0Y\nAiRt5dqA5jIIaCKGAElbuTag2QwC6mUIkDSObUCzGQTUzRAgaRzbgOYzCGiMIUDSNmwDms8gIDAE\nSJqAbUA7GARkCJA0IduAdjAItJshQNKEbAPawyDQXoYASX3ZBrSHQaCdDAGS+rINaBeDQPsYAiRN\nyjagXQwC7WIIkDQp24D2MQi0hyFA0nbZBrSPQaAdDAGStss2oJ0MAs1nCJA0JbYB7WQQaDZDgKQp\nsQ1oL4NAcxkCJE1Zbxtw3b0jJY9Is8Ug0EyGAElTtk0bsNo2oE0MAs1jCJC0Q9560B7s9sKiDVi/\n6WnbgJYxCDSLIUDSDtl5/lxOWm4b0GYGgeYwBEjaYd1rA2wD2skg0AyGAEk7zLUBAoNAE1Q+BETE\n0RHxw4i4OyI+WvZ4JBVsAwQGgbqrdAiIiLnAxcBJwKHA+yLigHJHJQlsA/Q8g0B9VToEAK8F1mTm\nA5m5BbgCeHvJY5LUYRugMf2CwJY1a8odmCZV9RCwN/Bg19cPdbZJqgDbAHWbKAhsOOVUG4EKm1f2\nALZjdDpPOuhl/8Whe17NC+b+ctDjUbcnYNeyx9BQV9/T9cU9u5U2jqk4AzhjbueLzcDnSxzMNCwp\newBN9O7uL9bCtcvLGkk7nDv94F31ELAWWNb19TKKNmBCu+++kHnz5rJo6TcMAJIkbUfVDwfcDrwy\nIl4RES8ATgWu6bfzY49tZv36TYzs8R62PLfzrA1SkqQ6mjM6Oq3GfdZExBuACyhai4sy859KHpIk\nSY1Q+RAgSZKGo+qHAyRJ0pAYAiRJailDgCRJLWUIkCSppQwBkiS1lCFAkqSWqvoVA3dYRBzN+OsK\n/HPJQ6q9iFgGfAl4GbAeWJmZKyNiMXApsB9wP/CuzHy8vJHWX+fOmbcDD2Xm7zjHgxURi4ALgYOB\nBcB7gR/jHA9ERHyAYk4XADdm5sf9GZ6ZiLgYOB4YycyDOtv6zmlEfAx4P/AM8LHM/N5kr9+oJsBb\nDw/NFuDMzDwQeAfwmc68ngPclJkHAzcDZ5c4xqb4Q4o3pbELeDjHg3Uh8N3MXE4RBO7DOR6IiHgx\ncBZwLHA48KqIOA7nd6a+CLy5Z9uEcxoRrwZOp3j/OwlYGRGTvs83KgTgrYeHIjPXZeadnc83ALdR\n3M3xBOCSzm6XACeWM8JmiIh9gLcC/wrM6Wx2jgckInYDjsrMiwEy85nM/AXO8aA8SfFzuxvwQmAh\n8H84vzOSmTcCj/Vs7jenbwcuz8wtmfkAsIbifbGvpoUAbz08ZBGxP3AgRfpcmpmPdB56BFha2sCa\n4R+ATwDdtwRzjgdnX2B9RKyMiP+JiIsiYiHO8UBk5pPA7wMPAOuA72fmLTi/w9BvTvdi/E32tvse\n2LQQ4DWQhygidqFoV87sPaaXmaM4/9MWEW+jOOZ3B8+3AOM4xzM2j6KmvrLz7wLglO4dnOPpi4gl\nwOeAVwOvAI7s/Fxv5fwO3hTmdNL5bloI2KFbD2vqImI+xS/PyzLz6s7mRyJij87jewIjZY2vAV4H\nnBARPwMuB94UEZfiHA/SQ8CjmfnVzl+tl1Mca13nHA/Ea4GbM3NNZj4KrAKOwp/hYeg3p73vgft0\ntvXVtBCwQ7ce1tRExBzgC8CPMvOCroeuAVZ0Pl8BXDXbY2uKzDwrM5dl5r7AO4FvZ+a7cI4HJjPX\nAWsi4ojOYqnjgeuAr+IcD8KNwGER8eKIWAC8Bfgm/gwPQ785vQZ4Z0S8ICL2BV4J3DrZCzXqFMHM\nfCYiTge+wvOnCN5b8rCa4PXAacDdEXFHZ9sngU8Dl0bE3XROUylpfE00VuE5x4O1guJ015cC9wB/\nSvHHkHM8Q5m5MSLOo/j9uxC4FvgOxZuQ8ztNEXE58AbgJRHxIHAufX4vZOaPI+KLwGqKUwTf0zlc\n0Je3EpYkqaWadjhAkiRNkSFAkqSWMgRIktRShgBJklrKECBJUksZAiRJailDgKRtRMRfRMRzU9jv\njRHxXOcW3mPbro+I7wx3hJIGoVEXC5I0UNO9iMiHBjoKSUNjCJDUz4Q3MtqezLxvUAOIiAWZ+dSg\nXk/SeIYAqWEi4lXA+RQ3JdqV4uYitwC/m5nPRsRewN91Ht8FuBP4VGbevJ3X3QW4gOKa8E8DXweu\nnmC/64HRzDyma9siikudHkdxg5P7gL/NzP/o2uc9wMXAIcDHgaOBXwDLI+Jw4K+A5RSXpH0YuDYz\nP7wDUyOphyFAap7/BJ4CzgZ+QnGP8bcAcyLiRcAPgccp7v+wEfgwcGNEHJOZ39vO6/5653lrKG7Q\n9dkJ9ht3a9POzbxuBhZTBIGfUdy9798jYmFmrux5/pcprj//fmBeJ3x8A/gx8MfAz4GXA0dOYS4k\nTcIQIDVIROwK7AecnpmXdD10eefxPwFeArwuM3/a2fZ1ijfY8yluFjXR6x5LcVvYj2bmhZ3N34yI\n2ybYfQ7j1xN8FDgQOLorZHw7Ig4G/jIiLum5ycnXMvPPuv7vg4AXUbQV3+3ar/v7kzQNnh0gNUhm\nbgRuAD4ZEe+PiFf27HIk8IOxANB5znPAFRS3ge23DmDsr+7/7tn+zSkM67eAe4EfRMS8sQ+K257u\nCfxKz/5f6fme7qFoD/4mIn4vIpYhaSAMAVLzvJdiDcBfAxkR90fEBzuP7QVsmOA564D5wNI+r7kn\n8ERm/qRn++1TGM/LgQOALRRrCcY+PkvRGLy8Z/+HJ3iNk4AHgQuBn0fEPRFx4hT+b0mTMARIDZOZ\nD2TmisxcQrGQ7vvA5yJif2At8BsTPG0PijfpkT4v+zCwKCKiZ/vhUxjSg8BNwGETfBxOsUah2zan\nJmbmXZn5DmB3ilbiIeCyzuEPSdPkmgCpwTLzrog4FzgNOJ7izfhNEfGazLwLICLmUizyu7VzaGAi\nN3X+PRbIru2/PYVhfAf4BPBgZq6fxrexVWd8t0TE+RRnGryR4rCCpGkwBEgN0lls948Ux/jvB14K\nrKD4K/8G4KfAB4BVEfHnwCbgD4BfBd7X73Uz81sRcQNwXkSM8vzZAYv7PKV7bcHfA+8EbouIq3l+\nXcGvAb+ZmZPW+hHxNuCDFGsFfg7s0xnzRqZ2OEJSH4YAqVkepnij/COKN8tfAncDb8vMOwAi4lCK\n6wScDyyiuE7AUZl5S9frjDvNr+N4ioDxKYpj+l8DPgJc27PfuOdm5paIOBI4CziBImw8QXGtgCsn\neG6vnwCbgXMo1iZsAm4Fjs3M/+0/FZK2Z87o6HSvDCpJkurMhYGSJLWUIUCSpJYyBEiS1FKGAEmS\nWsoQIElSSxkCJElqKUOAJEktZQiQJKml/h/Bh5P+BteymQAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x108b13390>"
]
}
],
"prompt_number": 5
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**If you don't know where to start, start with the vertices**"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# create the LP object, set up as a maximization problem\n",
"prob = pulp.LpProblem('Giapetto', pulp.LpMaximize)\n",
"\n",
"# set up decision variables\n",
"soldiers = pulp.LpVariable('soldiers', lowBound=0, cat='Integer')\n",
"trains = pulp.LpVariable('trains', lowBound=0, cat='Integer')\n",
"\n",
"# model weekly production costs\n",
"raw_material_costs = 10 * soldiers + 9 * trains\n",
"variable_costs = 14 * soldiers + 10 * trains\n",
"\n",
"# model weekly revenues from toy sales\n",
"revenues = 27 * soldiers + 21 * trains\n",
"\n",
"# use weekly profit as the objective function to maximize\n",
"profit = revenues - (raw_material_costs + variable_costs)\n",
"prob += profit # here's where we actually add it to the obj function\n",
"\n",
"# add constraints for available labor hours\n",
"carpentry_hours = soldiers + trains\n",
"prob += (carpentry_hours <= 80)\n",
"\n",
"finishing_hours = 2*soldiers + trains\n",
"prob += (finishing_hours <= 100)\n",
"\n",
"# add constraint representing demand for soldiers\n",
"prob += (soldiers <= 40)\n",
"\n",
"print(prob)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Giapetto:\n",
"MAXIMIZE\n",
"3*soldiers + 2*trains + 0\n",
"SUBJECT TO\n",
"_C1: soldiers + trains <= 80\n",
"\n",
"_C2: 2 soldiers + trains <= 100\n",
"\n",
"_C3: soldiers <= 40\n",
"\n",
"VARIABLES\n",
"0 <= soldiers Integer\n",
"0 <= trains Integer\n",
"\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# solve the LP using the default solver\n",
"optimization_result = prob.solve()\n",
"\n",
"# make sure we got an optimal solution\n",
"assert optimization_result == pulp.LpStatusOptimal\n",
"\n",
"# display the results\n",
"for var in (soldiers, trains):\n",
" print('Optimal weekly number of {} to produce: {:1.0f}'.format(var.name, var.value()))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Optimal weekly number of soldiers to produce: 20\n",
"Optimal weekly number of trains to produce: 60\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"sns.set_palette(\"Set1\", 8)\n",
"\n",
"fig, ax = plt.subplots(figsize=(9, 8))\n",
"s = np.linspace(0, 100)\n",
"\n",
"# plot the constraints again\n",
"plt.plot(s, 80 - s, lw=3, label='carpentry')\n",
"plt.plot(s, 100 - 2 * s, lw=3, label='finishing')\n",
"plt.plot(40 * np.ones_like(s), s, lw=3, label='demand')\n",
"plt.plot(np.zeros_like(s), s, lw=3, label='t non-negative')\n",
"plt.plot(s, np.zeros_like(s), lw=3, label='s non-negative')\n",
"\n",
"# plot the possible (s, t) pairs\n",
"pairs = [(s, t) for s in np.arange(101)\n",
" for t in np.arange(101)\n",
" if (s + t) <= 80\n",
" and (2 * s + t) <= 100\n",
" and s <= 40]\n",
"\n",
"# split these into our variables\n",
"ss, ts = np.hsplit(np.array(pairs), 2)\n",
"\n",
"# caculate the objective function at each pair\n",
"z = 3*ss + 2*ts # the objective function\n",
"\n",
"# plot the results\n",
"plt.scatter(ss, ts, c=z, cmap=plt.cm.get_cmap('RdYlBu_r'), label='profit', zorder=3)\n",
"\n",
"# labels and stuff\n",
"cb = plt.colorbar()\n",
"cb.set_label('profit', fontsize=14)\n",
"plt.xlabel('soldiers', fontsize=16)\n",
"plt.ylabel('trains', fontsize=16)\n",
"plt.xlim(-0.5, 100)\n",
"plt.ylim(-0.5, 100)\n",
"plt.legend(fontsize=14)\n",
"plt.show()\n",
"\n",
"plt.show()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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AWrduzpgxwzh5MpJmzcI5ceIYAAaDgU8//Yhu3Try8stN6NHjVVatWm4+xiVL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WJzWyuVWLOTViiVpGfnJC4/VSiVZObkJqxUqcjKy0lxdm5mwiqVitz89DZWkpdnbWdTwmq1\nkoJ8Y4rz8w1trKAgV5fi/BxNm+3Jyc9WthmXk5+lSFolJz9T1sYyCtKlKc63ipNWSsk3CQlrVDIK\nTCStlJJviCaXV0jJ14aTlktSrJGLyVcFE9bKxRTIA8lxmZh8iT9hg0KGpKmc7xpBEBjapvbk3S/t\nBMPRb1mjM+c6glSK5LnnES66JP5ALEb4qblED3/+4+5YZ342iUVi5+xPR0mHOjnRpdxlNoYQbEl1\nwJ3iWHv7Xan2pjrSWp/yjUMtzSn+/+zdd5QUdb7//2dX5xynZ6ZnhmGGJDmjCEhQFEFAEESSmEAR\n47rr3r13v3fd5O7edfeuaw5IDkpSMQEqKKgEyUFgCJPzdM7x90fPdtPt7+q9uwI6zuucOYfHfKqq\nq4vuqequd70r7Ml0yJXpoNOeYb/TkeXMcV+WPfaWDLtbMu3MsqOlOcuZ4/bmzPGW5sz1aWnKfL5N\nTa4MNzdnbr/GJm/W9GnH43Gamn2ZbvFnTt8SzLQ9lOkLuqIlEgmanJFMuy40NHliGW7Mtjfzjdzk\nF2WZTAcuKIglQWM48+3TGEk7Fk/gl2beFfqfzfDOZiyaZDGxMxBhx+mm72S57fnn095Ftj3/ShLx\nxEX7aStpU6d1vthzJPHTx18gpFKj8nn5+S9m8tL6bTgDIqxaEXfefC2L3/wYV0hEjhrmThzN0s3b\ncYcFzIo4cyaMYfl7O/DGxBhlcWbeMJLVW3fijYsxSKLMuH4kaz7cSQApeiHK1DHD2LD9CwIiCVrC\n3DxqGBs//YKwIEeVCDHpmqG889lewoIMZTzM+GFX8t4Xe4lJ5UgjQW4cOoQP9uwnLlcgjQQZO2Qg\nH355kIRcgSQUYMygAXx84CCCQoUo4GPkwAHsPHQYQaEkEfQxov8APjt8GIlSSdTnZVi/Aew5dgSJ\nUkXU6+HKfv3Zf/wYMqWSkM/L4N59OXjiGAq1moDHw8DefTj01SGUKhV+j49+Pftx9OR+NFoVbqeP\nfj0HcuLUXpQaGV5XmN49hnDy9Oeo1FLc7gi9ug/ldNlO1BoJLmeMnt2HUXZmOxq1gNMponv3ayg7\n/REatQinS6B7j5GUndyKRg1Ot4TuPcdQdvx9NOoETo+U7r2vo+zYu6gVMZw+BT36Xk/ZoTdRK2M4\n/Sp69LuRskMbUcsjuIIauvebQNmBdahlYZxBLT0GTaRszxrU0hDOiJHugydyZs9q1OIQjpiBnldN\n5fTOZWjEIZyY6TF0KmWfLEUt+HGKrPQYdgtlH7+KWuTHKc6l+4hbKdv6KqqED7c8n+6jbuX0ey+j\njnlxKfLpMXYmp958HnXUi0tdQM9xs/lo+c+xIeaIOMovfrcFjUbznby2Nx6oYcnnFQAUGZU8O6sf\nQhttyvZDOi2RqK4iMm8W/OPA35qLdNkqRPmX735IP6Tt933MpTitc90jb1+0He+Hf5vUJv4wiJ94\n4onLvQ7fWd7Z8ukTR+oE1EV9iUQi+H3V1EWsyHN7EgqFcDeV05iwosjvRSgYxN1YTos4H01hH8LB\nII6GczjlBeg69CUUDOKoO4dX1wFjaX9CwQAt1WcIGDpi7jKQQNBPS/UZIpZScq4YRDAYoKnyLIm8\nzuT3GEwg4Kep8ixiW2cK+1xJMBigobwMeYduFPW9iqDfT935MtSl3SkZMJSA30ft2TL0nXvSadAw\n/H4fNefKyOnem25XDsfv91F1pgxrjz70GDoCv9dLxelTFPXpT6+h1+D3+SkvO0lJv4H0H3YNPp+f\n86dP0rnfAAaOGInP6+N82SmuGDCQIdeMwuv1cObkSXoNGszQkWPwenycOXWCflf2Z+jIEfi8PspO\nnqL/Vb0ZPmoYHreXM6fKGHhVd64ZcxUej4/TJ88yZGhnRo4ejNvt59TJs1x1dTFjrh2A2xPg5Mlz\nDB9WyLXX9sbt9nHyZDnDh9q4dnTPpE9VMvzKHK4d2R23O8DJk5UMH2xizIguuNw+Tp2qZvggPWOG\nd04ur6ya4f3VjBlWitMd4NSZGob3kjHmqiJcngCnztYyvIeEMUMKcXmDnDpXz4iuAmMG2nC2eniX\nOKP75+LwBDhd3sjwDgFG987B4QtyuqKJ4YV+Rvcw4/AGOVXZzPA8N2O663H4QpyubGGExcXILloc\n/jCnq1sYobNzTYkWZyBEWa2DMWo340qtuIMRJHl9sOQVfCev7Q4mFe8erScaT+AORumWq8Vm+Ofa\n43/fo1bL8fvD3z7h9yAinR7RlVcRf/9diETA5yP+xS6EceMRKRTfvoCLkB/S9vs+Rq2W//piP8ay\nd08+QQIuxs+88Vdc9PW/FGlTp3U++LwMRV4XRCIBRVFPvjjZjMTYEZFIQDB2YU9ZC1JzCSJBQJLT\njS/POVDklCISBGR53TlQ4UKV2wmRIKAs6MGROg+a/M6IBAFNcW+ON/jRFXZFJAjoS/ryVXMAfYek\njZ37ccYZxFTcDZEgkNNtAOfdIXJKuyMIAnndB1DhC2PtlHRB78HUBGLkd+mBIAh06DuE+kgcW7ee\nCIJASf+raI5C0RW9EASBLoOvxpGAjj2SvuLKYXgEMR27J93zqmEEBDGdWsf7Xj2csERCl169EQSB\nAcNHEJVI6Na7D4IgMGTESERyGd1bfdXIkQgKge69k+tz9ahhSFUJeva+AkEQGDFmKFJVmF59uiII\nAiPHDEGhDtC7T2cEQWD0tQNQazz07VuKIAhce11vNGonffp0QBAExo7tiVbloE+vwqSv7Y5W0USf\nnsk6metGdUYjq6N392RdzthrStFIa+h9RW5yfHgHNEIlvbtZk+PDCtEkztO7qznpq/LQRs/Su5Mp\n6cE5aMOn6FWiRxBEXD/AjCbwFb2KdUn3M6DxHKFXB23SPTVoXYfpVaBOursKrf0AvWzKpLvI0DZ+\nSY9cBWJB4PpSKZqavXS3yBELIsYWitFUfEH/HB1iQcTMklwqd775nb221XIJ1/ewpryp/bLi703a\nu8i2pz3ffdrUwcnXvyfLenpZX4Mnsi7z/EfxbPoXWRayvy3L3nzf7OzlZ19m+rVxcdZ41vTC16bP\n7AKWvXxx1rgo6/lkTy9kjYuF7OX/3+bPvqo22+Ks5yvOfnxx9vpkLT+rCdrX1j9r/GvLF2WPp/+d\nSIBEEH2jxVmvL1Hiuy1cndQ3P/USPFLtSl3B057LH+HKoYh/98eUE0cOEf3FT0lE/7VGfO1pm2mv\nOfn2tKmDk+F9Cgk7kp8oQ43n6GlTEPMkb7QYd1dzRa6MiKcegKijgq5mCSFX0uGWcjoZxQQddQAE\nm8rpqBMRaEkuz193liJVAl9zDQDe2jMUKOL4mpJ2V50mTxrF05i0o+IUFiGMqyF587aW8lMYCeOo\nqwKg6exXaOMB7LXJKzrqy06giQaw1yTHa04dQxHw0VSdHK88cRSp30NjqyuOH0Hk89DQ6nPHjhBz\nu6ivSrrsyCHCLhe1lck6hZOHDuJ3OKmpSPrEoQP4HC6qW3304AE8di/Vlcn1Pbz/MK6WAFUVyedz\n6Muj2JtDVFYkt8fBL09gb45RVZncvl/uO0lTE1RUtHpvGU1NUiork8Wbe/aepbFZRmVl8tz87r3n\nabQrqaxKFv3uPVBFo0NNVU2yKHfPgRoanDqqapNFuXsO1dHgNlJVmyxS3nO4gQafmarWe87sPtpM\nQ8BKVX2yCHf3cTsN4XyqG5M78N0nnTREbVQ3J6tcd59y0UAHqluLcHef8VEvLkn7fIAGaWdqHMmi\n3D2VIeqVnalxJb8u310ToUHXjZrWOynvaYjSYOxGZWsTuS01LeQMTLfy/y5i1SkY1jndHr/925Pv\nV9q7yLanPd9dvn83hvgXMm7MUNYv/RUOiQhdTMS9jzzGb55eQsu5EAUWDfMXzubJZ5fT4AliM2m4\n+97Z/OH55TT5QuSb1Nxx90z+/NJK6n1h8oxq5t05g78sXkO1P0SuQcPtc6fx30vWUhkMY9WpuGfO\ndP62/HXOBsNYdUruu20az6x4g7JwBLNGyfwZU3hhzXp84ShmlYI7p9/MS69vwB+OYVLJmXfLZF59\nYwOBaByjSsHtUyazeMNGQtEYeoWc2ZMns3TjBsLxBFqFjNsmTGTlW5uSlsuZPmECq9/aSDSRQC2T\nMm38Tax9cz3xRAKlTMaUceNZv3E9UUAlkTBp3Hg2bVhHLJFAIZVw0/XjeeuNN4iLRMglUiaMHcem\ntW8hiEEiSBl37Xg2rNkAojhSiZLrx4znjdUbQBRDJlFy3eiJrFq5FkGIIZFouG70ZFYsX4VYiCKW\naBkzZirLVqxAEMKIxXrGjJ7GsjVLEYvCiKUGRo2azrK1ryEWhxFLTYwaPZ1l6xcjEEQsNTH6upks\nW/8SghBCIrMw8rpZLHvzheS4PIfRY2ez7O1nERJBxIpcRt8wl2VvPoMQ9yFR5TNq3DyWbvgbQtyH\nWFXA6Al3sOyNvyDE/Ii1NkaNn8fS1/+MEPUi1XVg5MQ7WLr6TwjROiT6Doy++S6WrngSIdyIzFTC\nyJvvZtmS3yOEG5GaSxh5y90sf/W3iEN2JNZSRk6fzx/+cheGuIhatYinBl79ra/Z/2tu7mdjZ1ny\nAG9nWTPzhnbAopF/y1ztuVQRz55LoqmR+NLFQLKLLDk5SO5/8DKvWXu+V4m1twP4trSpq3Xm3v/7\nRHU0eXO0RCJOoOZDdFfclLLv7BZMvSel7Dn1Pjn9kzf6S8Tj2I+/g23ILSk3H36b4uG3plyzZwOd\nxsxMuWLXerrdMDvl89vfoNdNc1M+tXU1/SffASQvnT3+3kqG3JK8MV88FuPg5pUMm3F3yl++uZzR\ncxak/Pm6JYy9/b6Ud6x5lfF3LQQgFovx0YpXmHzPopS3LHuZafc+kPLm117itoVpb3r1ReYuejDl\n119+nrsefCTlVS/+nQUPJZcXjUZZ9uJz3PfQgpRfe+5l7n/0zpQXP7+EBx+dlfJLz6zikZ/cmvLz\nz7zBY49NSfmZp9/ksUdvanWMp/+2mcceuiHlvz37AT9ddF3aL3zIY/eNTPnvL3/CT+YPAyASifLs\na5/z6J2DWx3jmaV7+cnt/VN+duUBHp3ZJ+21R3h0eo+kozGeXXeCR27unPLzb5Xx8ISOAIQjMZ5/\n7zyP3FCU9pYqHh6VvBFgOBrjhR31PHi1Ne1djTw0xNLqOBsivRl/V/pmcd9V/m3jMY63foM0tb+N\nO4d1/M4f43Lmh361yeXuIvtD336XO5fiap3RCzZctB3v9pdvaRNX67Sp0zrNnvT/t0gkEBVrMxyT\n6DJ9QR8KkSCQkBsyjCLTgsqUYbEm0xKdOcNSnSVlQRCQGy6wWIzSmGmVKSfDapM1w1pLbspisRhd\nTqYNWTZarRk252aO5+TlZzk9vUQiITfbNkum840Zzs+yzabPdL7uAovJz09fZisWC9hy1Zm2qjKc\nb1Vkzm+RXWCBfLM0w3nGTOcb00UnErFAviH9HhYLAnkXtCWRiAXytVlWpT/tSASBfGXsgvlF2BRp\nyyQCikC6j8x3mSn905epbjnegD8c+4ap23OpIxKJEP/qN4iuHp76XezJ3xL/aNtlXKv2tOeHlTZ1\ncJKjE6XO7ybiMaQxd4YlUVeGxWFnpoNpx+MxCDgyHPfZMxzztmQ46m5KOxYj4m7OcMiRbp4Vi0bx\n2xsz3ZJpb3NDhj1N9Rl2N2aOOxrqUo5Go9gb6zPcXJ/pxtqaTNellxeJRKivzXZzhutq7BmuyXCU\nmhpXlt0Zrq31Zrred4Fj1NT7M1zbGMocz3JtSyTT9nQxYiQao8ae3omHIzFqnInM8fTqEYnGqXGn\nD14isTg1fvH/6GgsQW0ofZY0FI0RVKcP7r7LDO5opMCQPFDzhWNsO9HwLXO051Lnf+wiu7+9i2x7\n2jvE/m/Spk7rHD9+LnHPHb8lpFChCvr46/M/5bdPL8MZFMjTiXj8/jn87tkVuEICVo2In907iyef\nX4k7KsaiTPDYPbP4r1dW44lKMCsTPHrHDJ5ashZfXIpJFueBudP57+VvEEhIMUhjLJo9jadXrico\nkqETR1h42y08s2YDEbECjSjMgulTeOGNTUTFClSEufuWyby8/k1iUgXKWIg7pk5m8aa3SEiVyGMh\n5ky6ieWb3yEhVyGPBLhtwk2semczIpUGSdDPbRMmsPq9dxGUasShANPH3cjrH7yHRKmGoJ9bxt3I\nhg/eR6rWEA/4mDx2HG9t+wCZWkPU52Pi2Bt456MtKNQawj4f46+9nvc/3opSqyXs9TJuzFg++PgD\ntHotXpeX60dfz7bt76LWqfG5A4wdfSMf7ngbjU6Jzx3i2lE3sf2TjWh0CrzuKKNHTmLHp+vQ6WR4\n3HFGXnMzO3euRaeT4nKJGDFiCrt2rkank+B2CYwYOZ2d25ej04lxeyWMGDmDXduXotWAyyNnxOgZ\n7ProNXQaEW6/guGjZ/LZh6+iVSdwB1QMHzObz7a+hFYZxxXUMOK62ez64AV0yhjusJ7hY+fy2bvP\noVVEcUcMDB83j11v/R2dPII7bmL4jXeya9Nf0ckiuLEwfMJd7Fr/FDppCLeQy/CJ97Dr9T+hkwRx\nS/IZPmk+O1f9EZ04gFtmY/iUBexa8SRagniUBQyfdi+rnrkHm0TCMSL88Q/bkclk3/7C/Sfy/rF6\nnt9xDgCrVs7Lcwd87eqjH2ra0mmJhN2ebNLWWqiOVodkyQqEzl0u2mO2pe13OXIpTuuMunv9Rdvx\n7lg8rU38IWhTBydPPrU48c7uIFKtlbC9io6WBmrjXRCrLMR9tRTIqqiTdEOithD31JAnqqBZ2QOJ\nJoeoqxpr9BxuQx9kOitheyUGfxn+nP7I9VaCzRVo3acI2QahNObibyxHZT9JvHgwKlMu3vrzyBqO\nI+l2NWpzHp6as4iqj6LsMRyNJQ9X9Rmi5YfR9bkGbU4+9orThM4exDpoNDqrjebyU7i/2k/B0Osw\n5NpoOHcK+7F9dBwxFmNeAXVlX9F8dA9dRo/HmGej9vQJag/upud1EzDn26g8eZzKfZ/Tf9xNWPIL\nKP/qOGf3fsaQG65R33MAACAASURBVCeSYyvg3IljnNr9GcMmTsaaX0DZsSOc+GIX106eSm5BAaeO\nHubQZzu5YcpU8goKOXHkMPs/3c6Nt0wkv8DGscNH2ffJLiZNH0deQR5HDx5n9ye7mTJjNLaCXI4c\nPMmuHfuZfttwbAVWDh88zafbjzBj5pUUFFg4sL+MT7afZPasvhQUmNm//xwffXyOOTN6YrOZ2H+g\nnI+2VzBnelds+Ua+PFDJxztrmDOlE7Z8PV8eruHjnXXMmVxEfq6OL4/Usf2LJubclE++Vcu+I/V8\nss/F7HEW8q0avjzWxI4vPcy+Vk9+joa9x5v55JCfOSOU5FvU7D3p4NMTUWYPlZBnUrH3lIudpxPM\nHiQiz6hg7xkPn5aJmNM/Rp5Bzt5zPj49L2FOjyB5ehl7K4J8Wq1iVicPeTo5e6uC7GrUMMNmx6ZT\n8lFlM6LBixgw7LqL8loPRmLctWw/nmDy26HHb+jKiC6Wb5nrh5G2tnO91F1k29r2u9S5FAcnI+9c\nd9F2vJ8smd4mDk7a1Gmdzw7VItUmv0qXmYo4WRNBrEr+wRbUNk41RJCoW60toKw5jkSTrPOQ6As5\n7wCZ7h/zd6DCLUKuT1phKabKL0ZpTNZtqKwdqQ0KqExJa/JKaIjJUZvzANAWdKIpLkdjSVpf2Bk7\nCrQ5yToPU3FX3GIVOmvyD5SlYzf8cg2G3KRzS7sRVGowtnYYze/SnbBajzEvOW7r2oO4Ro+59Q9c\nhyt6IugNWPKT03fs3hOpwUiOLenSHr2QG01YW8e79OqDxmwmtyDpbr37ojVbyCsoBKBHn74Yckzk\nFySX36tvb4xWHXkFyefTu39PLLlqbAXJ59+n/xVY8xTYCpLbq2//ruTmSSkoSG7vAQO7YLOJKChI\n1uUMHFiKLTeOzZas2xnQvxibNYqttW5lYP8ibJYQtvxk3crAPjbyzX7yc5OFIQN752Ez+ci3JgtD\nBvXOJV/vIt+arGMZ2NNCvsZBfk7Sg3uYKVC1kG9J1rUM7mYgX95AnilZ1zKoiw6bpI48Y/J0yaBS\nDQXiGvIMySthBnVUUZCoJE+f/CZkUJGcgmg5ebrW8QI5BYHz2HTJrq3XdrDgOLaDixWFVMyE3nkp\nbzpY237J6vc0osIiJM+9BOrWmqrGBiKLFpBwOb95xva050ecNnVwIs5+NonMQsFEPKtwMJY1nshq\nmBTPvNwrkTV9PHv+WPQbHY9mj2fOH/u28UjmeCwayXA0azwayRyPf8v0X1te1vpkO5I9Hslc30iW\nvzZ+wd11RSJRxvQikShjPPn4WY5kOnv6SOxbnPH4meMiEYSzfOHDJadPZE6f1QAplri4H2Am9M5D\n2to5rqzRy4m69k/L39e0d5FtT0bi8Yv300bSpu6t43E2P/Hl3lMISh2RuhOMGGihrslFQqJB7D3L\n0K46aps9INUgcp1hSCcNdc1ukGnAfpoBRSoaHB5ECi3Rhq/oVyCnweFDUGoJ152gV66UJpcfsVJH\noPoYPcwSmtw+JCo93oojdNGJaPEGkGj0uM4colQNdq8fmdZAy+kDdFAmcPiDyDUGmr7aT4E0isMf\nRKkzUHd8P1YhgisQQqk3UHV4L+ZECHcojEpvpPzAHoyxAJ5QGLXRxNl9X6CJBPBFImgMJk7u+QxF\n0Is/EkVrNHF89y4kAS/BaAyt0cSRz3ch8nkIxqLojWYOfvYpcY+HcCyGwWRm385PCLvcRONJ796x\nnYDTTSwRw2Ay8vmOnfjsPuKJCEazgV3bv8BjD5IgjNGs55OP9+JqiZEgiMmsZ8dH+3G0iIAgZrOW\nj7YdorlZgkjkx2zWsG3bcZpblIjwYTar2fbRSZodGkR4MZvUbP34NM1OPaKEB7NRxbYd52hymxBw\nYzYo2PppBS2+HERxJ2a9gq27qmkJ5COKOjHr5Wz9vI6WUAFCzIFJJ2fLnkaao0UIYTtmnZQt++20\nUIoQbsakkbLlkAu70Bkh1IxJLWbLUS8t0q4IwUZMKglbTgSwK7sj+BswqQQ+OBWmRdsbwVuPSSmw\n5WwUu6EPEed5cpQyVp6upcv1izBb87/1dfvPRiEV0+gJcba1U6wnGOWarj/8Uztt9d4wosIi6FBM\n4sOtyV801JM4W4Zw3Q1f6/78r6Stbr9LlUtxb50lG45dtHvr3Dm1V5u4t06bqjnZtetg4tEH/xt3\nLIxRLOPxX83lhRXv0NDkorjAwl233cCLq9+nvtlBh3wzd986jhfXvk+D3UWHXDN3TL2OVzdspdHu\noijPzO2TrmXJm9totLsptBqZM/Falr69jSanh0KLkZkTRrPi3Y9pdropsBi59fqRrPpgOy1uLzaz\ngWnXjeD1rZ/Q4vaQbzYw9drhvPHhThxuD3kmA5NHXc2mj3fi8PrJNeq46ZqreWvHZzi9XqxGHTcO\nG8o7Oz/D5fVj0WsZd/VVvPfZblw+HxaDjrFDBrN1z27cXj8WnZbRgwfz4d49eHx+zDodIwcOYvu+\nPXj8Pow6HdcMGMQnX+7FGwhgUKsZNmAQnx34El/Ah16j5cp+A9h98EsCwQAapZrB/Qaw9+A+/AE/\nGrWWQX37s//QbgIBPxqNnv59BnDg0OcEgj7UKj39+wzhwKFPW22gf9+hHDy0nWDIg0pppG/v4Rw5\n8iGBoBuVykzvXtdw9MgHBP0elBoLvXqN4tjhDwj4XSjVOfTsNZqjh94hFPSgVFvp1edajux/i5Df\njVKbS69+Yzmy701CARdKTS69+o3jyN4NhAJOlDobvfqP48juNwj5nSh1BfQaNIHDu1YT8jtRGYvo\nNWgiRz5d2eoO9LxyIkd2LCfkc6AyFdPzqskc+XApIZ8dlbmYnsOmcmTrYkI+B0pTR3pdM40jH7xM\nwONAZS2h98jpvP/6fyIPxWlUi/jl/3sHrU7/7S/cfyFVdj/3rz4EgAh4YXZ/Cow/7BsCtvWaidiq\nFcT+/IeUhSnTEP/nrxF9R3eZbuvb72LnUtScXDNn7UXb8X668rY2UXPSpg5Obr3zN4m6ULoK3t+w\nA23HsSl7az5C32UckGyU5Kv8CFPP8Sl7Tm8hp99NKTuOv49t8OSUmw6/Q9HQKSnX799M6chpKVd+\nsYmuY2akfH7nBnrccFvKZz5+gz7jZ6d8cuvrDJo8J+XD763hqqm3p7z/7VWMuPWOlHdvWsHomXel\n/Pn6ZVw/956Ut69+jfHz5qe8beVrTL5zQcofrFjMLXffm/JbS1/htvn3pbzxtZeZc+/ClNe++iJ3\n3Jf2qlee5a6F6cdf9tLLzL8/vb5LXlzCvYtmprz4+RUsfGB6yq+8sIYHHkxvzxee3ciDD6S3/7PP\nbObBhTek/fx7PLjg2rRf3MoDd1+T8nOvbueBO4elvXgnD8y7MuXnl3zGolkDgGQTvBdW7GfRjD5p\nrz3Eoqk9W53ghfVHuH9yt7Q3nWDRjaUpv/huGfePLU77g3MsHF2Y9odVLBxuS3l1Qwcm3P3vXOz8\nevMJvqxI1i/c2CuX+0d1uuiPeTHzY9i5Rv/2l1QXWQBhwcLvrIvsj2H7XcxcioOTEbPWXLQd787V\nM9vEwUmbqjlx+zPPt8VEmZ8gY0K6yZdIJCIuybI008g0mZZrMyxSZFqs1GdapcuwRJU5LtVkWq7N\ntEJnyLBSZ8y0PtNqQ6a1xm+23mjKtCnTJrM5w0aTMWtc/822ZD5/iyVze5nN6e0NYDapspz5/2c2\nZt6C3pJlszGzjbtZn76MVyQSYTZIMmzRZd69wazNvDOgRS3KcubbJeeC8QQJcpRpC4IIZeLS3Jhv\nSv+C1L8/+qoJVyDyDVO35/sQ8cM/Qbhpcsrxl18gtm7tZVyj9rTn+5U2dXBSaJWlil5j0TAqwXuB\nQ6hE7gwr4860IyHk0UxLI85kMzYgGg4iCbRkWPCnHQkFwdN0gQMk3E2potlIKEDU2Zh2MEDYUZ9y\nOBgg2NyQcijgx99Ul2FvY23KQb8fT30N8dYCqKDfh7M27YDPS0tNdYabL7Df56Whuiptr5f6ysqU\nfV4vNRVpez0eaiprLrCX6vL6lD0eL1XlDRmuLG+6wD7Ky1tSdrt9lJc7L7Cf8kr3BQ5QXuHNcEW1\nP21PgPLqQMouT4CKmuAFDnK+Lpy6gsXlDXK+PnqBQ5xvjKfs9ocobyE97gtx3iGk7Y98zWddkvT8\ngSjnvGnbfSFiug5civQu0FGakzzQC8fivH+s/lvmaM/lTnsX2R932puwfXva1Gmd8vL6xK2THiUs\nVaGOBFm28Y88/Is/4woI5Jkk/PE/H+bhXz6FOygm3yDmyV8+xKO/+iueiASrTuDJf3uAx377t6Q1\nIn73+CJ+9vun8cel5KhEPPHYQn7+x78TSMgwK+BXj97Hfzz1LAHkmGRxfvnQvfzyr88TFuQYpDF+\ncf98nvj7i4TFCgySGI/feze/efYlolIlWlGUn86/kydfeIWETI1aFOGRu+bxp5cWk1CoUMUjPHjH\nXP6yeAkihRp5LMwD8+by368tQVBpkEVDLJwzh78vW4pEpUUSCbJg1myeXbYMmUaLOBzkrttm8dLK\n5cg0WggFufO2mby6agUKrY540M/tt87ktdUrUGr1JEIBZk2bwfK1K9EaDAS8PmZNm8GKtSvQ6g2E\n/H5mTL2V1euWo9FpCflDTJ9yG2vWLUFr0BDyRrhlyizWrnsVvUGN3xfjlpvnsG79S+gMSvzeBFNu\nnsf6Dc9hMCrwekTcPPkuNqz/O0ajHK9PwqRJd7Nx/dMY9BI8PhmTJt/DpnV/xaCX4vXLmXjzAja9\n/hQGrRhvSMXEKfeycc0fMeoEvCENE6fcz8bVTyYd1jJx6iI2rvwtRg14owZuuuUBNi3/NUZ1Am/c\nxE3TH+LNZb/CoIjjE+Uw4daH2LT4lxgUMXyClZtmPsKml/8dgzyKX5rPhFmPsumFf8Mgj+CX2Rg/\n+ye8+dzjGKRhfMoiJsx9jL89eQsFchnHE2Ge+eOnCN9hoeM3ZcepJv6yrQwAg1LK4nkDkUl+mJ89\nfkynJRJ+H9H5d5E4fjT5C5kMyYuvIgwY9E8v88e0/S5GLsVpneEzVl+0He+u12e1idM6berg5Gf/\n8bfEzkNyxHINEX8LZuUp3NKBiGUa4iEn2sQxvJrBSGQaYkE72tAR/Jarkcg1RP0tqD0HieSPQCLX\nEPE1o2zZT7x4JFKFhrC3GUndHiRdr0Wq0BJyNyFU70bZ83pkKi1BZyORc7vQ9bsRmVpLwNFA4NRO\nzFfehEylxW9vwHtsO/nDb0au1uJtqsN+8COKx9yCQq3F01RLw75tdB47HaVGi7uxlurdW+l+460o\nNTqc9dVUfLaFfpNnodLqcNTXcPrjdxgy7XZUGi0tNVUc/3Azw2+bh0qrpbmmiiNbNjNq5jzUWh2N\n1VXsf/9Nxs29C7VWR31VBbvf2cRNd9yDRqujrrKCnW9vYtpd96DW6aipKGfHW5uYcc8CNDodVefP\n8+Gb65m74C40Oi2V58t5f+NG7rh3LhqdhorzFbyzfjN3LpyBTqeh/HwVm9e9z/xFN6PTqTl3tpo3\n121n4aIbW13DxnW7eODB69BqVZw9W8cba3fz8IOj0GiUnDlTz+uvf8nDC69Go1Fy9lwTa9cf4uH5\nQ9BoFJw518Trbx7noTv7tbqZ1zef4uF5vdCoFZSV21n3zhkentMVtUrO6XI76z6o4JEZnVCrZJyu\ncLLhw1oemlKUdJWLDTsaeOimfNRKGaeq3GzY1cJDN5hRK6WcqvGycY+Lh8foUCmknKr1s+mAj4dG\nqFDJJZysD7DpUJCHBstQySUcrnNRlTeVq6+fekle+9FYnPkrDtDsTV6l8eCYTlzfI/db5vp+5se2\nc03Y7UTumA2VFclf/ItdZH9s2++7zqU4OBk2fdVF2/F+tm52mzg4+WF+tPofcvSUA7E8WSciVZmp\ndUgRt9aNCHIDdW4pklaLFSbq/QokrdNLVGYaA8qUpWoLTRElUkXSMo0Fe0KLtLXORK7LwSXSIlMl\nrTBY8Uj0yNRJK425+GSG1LjKlEtQYUTeOq7JySeqtaBotTbHRlxnQalJWme1gT4HpSZZt2HIK0Rs\nykWlTdqYV4DMko+qdXpzQRHKPBsqbdKWgiJUufmoW6e3Fhahz7OlnFdUjMFWiKbV+R2KsRQWotYl\nXVDcEWtREZpWF5WUkFdkQ6NLLr9DSUdsHfLQ6JLbp7ikmIJiK7pWdywpoqijCZ0uebqhtFMhHUv0\nF7iA4o4atNpknUlpaR4lHVVoNMk6k06dcintqEi5tMRCSaEUjSZZZ9KpxEJJgfgCmym1idCok+5c\nbKQ0P45alaxD6VJspFNuDLUqWYfSpYOeEks45c4FWkqMIdTK1vECLaUGP2pl8uaBXfLVdNJ5USla\nnaekk9qNSp6sW+mSI6eT3Jly33w9weqDXKpIxAIT+6QvW37zYC3xNvTBoy1HZDIhff5l+EeNl8dN\n9P4FJOpqL++KtefiJRa/eD9tJG3q4EQmzfpFIrMwUBQPf6OJhzIdzXIkmDn515w5fTycOR7LcjTo\nz3JmQ6ZI1ni2w4Es+zILMMP+TAezpg/5Mx3Imv/rzpze58tcX//XxoPf4vT2EolE+HzhDHu9mfb5\nI5njWfb5o1nj3+JAZtM3X/BCgzfLnkCWg+k/BIIgwhPO/MMQjmcW3F7s3NAzF6U0WdRb5QhwoKK9\nA+kPJe1dZNvTnsy0qdM66zZsTfzXUx8Q09qQuCqZOr03Wz6vxhszYpTbGXNlEdv21eFLmDBImhk9\nqIhtB+sJSizoEk2M6pvPx0ebCMqsaGP1XNMzj09OtRCWW1GF6hh2RQ6fnXESVeeh8NcytKuFPeVu\nElobEncVg0vMfFnjRmQoQHBU0r/IwKHGAGJTAYmmcvrZ9Byzh5BaiojWn6V3rpavXBEU1g6E6s5y\nhUXNWU8EVV4x/qozdDGrOe+PobUV46koo9SgpCYiQl9YjPPcaYo0chrjAsbCEprPfkWBSkYzEizF\nJTScOkGeUoZLJCGnYym1J49jkUvwS+Tkl3Si4sRRzDIJQZmCgtJSzh8/hl4iJqZQUFTaibKjR1CL\nxYiUSoq7dOHk4UOoRCIkWgUdO5Vy4vBRFAjINGJKunTk2METSBIylPo4pV06cPTgacRxBRpDmE5d\nCjm0/wxCQofO4KVLFxsH9p8nETNiNLro2i2X/V9WE4uaMJkcdO1sYd/+WmLRXEz6Brp2MrPvQAMx\nCjCpa+jayci+Q81ERTbMymq6lOjZe8ROXFKMWX6eLsU69h13EZeUYpKcpksHNXuP+0goOmMSfUWX\nQiV7TwZJqLpijh2nc4GcvWUREuorMIcP0zlfxp6zMdD3xOTbT+dcMfsqRCRMfTG5dtM5R8TeaglY\n+mGyf05nC+ytk4N1IELl2wzI0bGhspEJc1+gsLj0kr4HXt15nrcOJ+9O3adQz+9v7nlJH/+7yI/5\ntER8726i9y+A1u7Lor79kbz4KiLl/753zY95+30XuRSnda6+eflF2/F+/ubtbeK0zqX9aHeRo1DI\niQe8+IPn0MbDaDUqEhEvQacLcmTotRoSYR8Bjwu9SYpWrSIR8uJrcaHVS9CqVcRCHjwOFyqtGI1a\nRdRfjrvFhVwtQqMqIRqoxu08jUwlRq1UEfFW4WpxY1YlUKsLCHmr8To8GGUJtGobIVcdXrsbozSO\nRp1PsLweu9ONThJDpbISqGzE7vSgEaKoi8x4q5tpcR1HTQRNUQ7+2gocbi/KeAh1vhlPQzUOpxt5\nPIzKYsBVVUeLy4MsEkRhKsRV24DD5UESCaI02qiob8Dh9SIEA6gN+dQ2NOL0eEgE/RTk51PX3ITT\n4yEe8JGbl0dlSwtOr5eIz0tObj41zS24vF4ifj9mq5WGJjtuz3GC3gD6nByaW5pw+07i9wbJN+tp\nbqrH4zmN3xsi12ymqbEFt+cMXk+IXIuKpsYGPN5zeDxRLGY1DU21eLzluD1xLGYNjU1VeLwePF4B\nk1FNY3MAj78KT0DAZFLR5AjgOebFE5BituhotAfw+H34/FJMuRoam0N4fLV4/QpMuWoam8J4/F68\nQSVmo5rGxgie0z68ITUWi5aGmihunw9fRIvZqqWhKYLb58Ef0WNSaWlsjOE+78UXM2JSa2isjeP2\nB/DFTZi1ehqrE7gqfPgEBWaNjvP+IJHaKK5IFKlc8e0v2u84k/rms/lIHfEEHKl2ca7Jl7qSpz3f\n/whDrkL8+z8R+/ljACQOHyT6i58ieeppRJI29ee6Pe35xrSpb05uvu0/E/We9CfVgPMzNLZRKfub\nd6HrOCZlb+0O9J3TTdo8FR9j7H59yq4zH5LT+8aUnae2YhtwU8qNR96naMjElOsOvkfHq9O9C6r3\nbabzNVNSrvjiLa64bnrKZ3ZspPcNt6Z88qMN9Bs/I+XjW9cxZNLMlA++9zpXT5md8r631zBi+tyU\nv9i0ijG3zUt51/oVXD/rjpQ/XruMCXPuTHnL6qVMvv2ulN9btZSp8+5O+Z2VS5hx5z0pb1y2mFl3\nz0957WsvMPee9PJXL36FefPnpLxy8RLump9+fsteWcU996YLRJe88gYL7k1vv1df2sDC+8al/OIL\n73Df/PT/z0svvs+9d49O+5Vt3HvHNWkv/pgFc4em/PLST1kwe0jaKz5nwW0D0165lwXT+qa9eh8L\nLvim4eX1h5k/8YqUX9l0jPk3JosUE4kEr75zkvljS9J+/wzzRxWmvOpcLjfe8Usudf5ryyl2liXv\ngDuqWw6Pjf3nCisvV9o/+f//dJGdOh3x/3vif9VFtn37/Wu5FN+cDJ247KLteL/YPK9NfHPSpmpO\n/JklDcRF8m+2kPlVaVycOY5E+Y0WSTMtyL7FisxPsJIsixWZTcikqsxxWbbVmZarNRlWZPkfxbb/\nyD+KZ1POGtdkjas1usxxXea4VqvJcub66fSZz0+nTW+fRCKBXq/IsE6Xaa1WnjmeZa1G+o3WZVud\n/iQaj8eznECnEmdYr5JcMD8YsscV6b8JIpEIBZfn/iZT+qWbsu0sa6bZG/qGqdvzfYx49lyEO9If\nFOIb1xF78bnLuEbtac+lTZs6OOlWoibWWsQaDXswa0PEoskjlljEi1kVINZaxBoNezDLfWkHPRgl\nvlTRajTgwiDypMYjfifahIto63jY50QddWZYEXakHPLYkQftyeZsQNBtR+ptJhJKFpEGXC2I3I1E\ngmnjaiTcap+jhZi9PmWPvZlwcz3hYHJ5npYmAo11qXF3SxO++pqUXc2NuOtrCLXa0dSAq7Y67cYG\n7FVVhFrvitrS2EBzdSWh1uU3N9RTV1mRcmNdLbWV5QQvdHlVyg119VSW16Zd20Dl+XqCweT/R21N\nA+Xnmi5wI+fP29OubeHsWRehUHKHXlPTwrnz7gts51yFj1AoWQRbU+vgbGUg5eoaJ+eqw2nXuThb\nE7nAbs7UxAiFkufyq+s9nK2LEwq3usHH2UaBcOudkasbfZxtkaTd7OesQ5pyVXOAM055etwe4qxH\nlfKZJg9ia3cuR7rkauhpSx5IxuIJNrfWoLTnh5WvdZF96fn2LrJtJIl44qL9tJW0qdM6lZWNialj\n7ycoVqBLRFj13t9Y+OhvcHqhIEfOU0/+nPsf+x2ugAibWcaff/szHnj897iCAnkmKX9+4qc88O9/\nwBMSyNNL+dN//oSHfvlHPBExeToxT/77ozz6xJ/xxSRYNQK/+/nDPPabpwgkpFiUIn79swd5/Mm/\nEESOWSniV48u4t/++FdCggKzQsQvH1rIfzz1NGFBgUGa4D8evI//99eniUpV6MUJfrHoXn71338n\nJlWiEyd4fOECfvP0MyTkKtSiGD+9dwG/f+ZZEgo1alGMR++5hz889xwipQZlPMJDd9/Nf734IhK1\nBnkswv3z7uC/X3kJiVqDLBbl3rnzeHrxy8jUWiTRMPPnzOPvi19GqdUiikS4Z/btPL/kVTQGPbFA\nkDtnzeWlpa+i0umIh0LMmzmXV5YtRqPXEwsFmTNjDouXv4pGryUaDDN7xlxeW/EiOr2GSDDGzFvn\nsXTlc+j1KsJBmDH9TpavfAa9QUEwIHDrtLtYtfpp9Ho5wYCEadPuYc3qv6A3yAn4pdwy7V7WrPoz\nBoOUQFDB1FvuY83KP2LQSwmElEy5ZSFrV/wBg05MIKJhyrT7Wbvsd+h1YoJRLVOmP8Capb/GoBUR\niBqYOuMh1rz2KwwaEcG4kSm3PcyaV36JQQ0hwcLNtz3Cmpd+gUGZICS2MmnmI7z+4i8wKGOEpPlM\nmvUorz//c/SKGCFZHpPn/JTXn/kpenmUsLKASXN/xp9+O5kClZyTiRDPP7nzO7uZ2/81e87b+d27\nJwFQy8S8dscgVDLxt8z1/Uj7aYl0EpEI0UcWkfhsV/IXgoDkqb8hjLnuf5ynffv9a7kUp3WuHLfk\nou1493xwZ5s4rdOmDk7uXfRkYv8JI4IgJRYNoBQfIKIYhiBOWh7fR9wwMumIH6lvDwnr6Fb7EDs+\nR1Q0NumQD1HzTmSdbkSQSIkGfcSrt6PqPh6xREY06CNy/iN0fSYhlkiJBLz4T2/DPOjmpP0e3Ce2\nkD9sOmKJlLDfg/3AuxSOug2xRErI56Fh71t0GjsbsVRKyOemZuebXDF+DmKpjKDHRfknm+g7+XYk\nUhkBj4vTH25g4C13JO12cfyDNxg68x4kEik+t5PD76zlmjn3IpFK8bocHHhrDWPvXIhEKsXjdPDF\nupWMv+f+lD95fTlTFjyIRCrF7XDw8dpl3LrwISRSKS57Cx+sXs6sRQ8hlUpxtjSzeeUy7nzoEaRS\nKY6WZjYtX8I9D7e6uZk3lr7CfT9ZiFQqxd5sZ82S5Sz6yV1IpVKam+ysfm0tD/10TsorF2/k0Z/N\nQCKR0NTkYNlrb/P44zcjkUhobHSw+OUt/NvPb0IiEdPY6OSVV3bw859c32oXr7z2KT9/eEzSTW5e\nWfo5jy8ahLZQzQAAHUlJREFU3moPr67ay+P3DUUiEdPQ5GHxmkM8Pn9g0s0eFq89yuN39E66xcvi\n9ad5fPYVSCRi6pt9LNl8lsdv7YJYLFDf4ue198t5fGrHpO0Blm6t5mcTbIjFAnX2AMs+aeRn11sR\niwWq7T52R4YyetLtl+W9EE8kuH/VQWqcyW+y7hnekcn9bJdlXf6vad+5Zub/2kW2ffv9a2k/OPl+\npE2d1jlX7kMQknUFYokSp0+JIE7bFVCnLVXhCl9oNa6YNm25Gm9ChyBJWqJQ4xf0iCWylANiA+LW\ncalSQ0hmTFulJaI0pyxTaYmqc1KWq7WgsyKW/sM6RHorYmly+QqtHqkxF0mrlVo9MnNe2jo9ipx8\nJK3LU+sMqHMLkbQuT6M3oskrSFlrMKK3FWbYXFCUss5oxFKYtt5kxlrUAWmrDWYL+R3SNpot2DoU\np22xUNixKGWTxURRx/yULTkmiktzM11iQdJ6BYLFYqCkxJRyTo6BTp2MSCTiVuspKdZcYB2lF9qi\npaRIeYE1lF5gq0VDaYEsbbOG0nxJenqjik55QnrcpKQ0B8Ti5FvEalTSyRJP26Cgkymatl5OqT6S\ncqFJDc5zXK4IIlHGwcjbh+uItaGvfH9MEanUSJ55AYpa79UUDhN9+AHiZ8ou74q1559PPH7xftpI\n2tTBiSbrrrECwW92IsvxzKZiolimiWTdZTaS2XQsEc4cjwczHQt4Mxz1ZX66iWaNh/2Z42GfO8uZ\n4wF3ZsOmoCdz+oDHlWGf65vtzWoA5b1gPJFI4HY6M+xyurLszrDT4cm0M3P7OB2Zttszt4fTlfn/\n5XBm2ukOZY1nFqTaXVnjnswmb3Z3ZlO3Fs+FTdvA7s1swtZygQVBhN2fdiKRIJBI3xX5cmTMFTno\nFMmDvUZPiM/PtlzW9WnPPx+RyYT0hVfau8i250eTNnVaZ9uHXyR+8chiglIt6oiLhY/fxIp1n+P0\nSrEaYtw2dSgrN+3GFZCSo4sy/aYrWb15H+6QDIs6xLQbh7Dmg/14InIsyjDTrh/A69sO4omrMMkC\nTBnTnw3bD+FNqDBJAky6ph9v7jyKX6RCJ/IycXhf3vr8KCGxBk3Cy4Sr+/DOnuOEpTo0MTfXD+7J\nB19+RUShRxl2cd2A7mw7fIq40oA86GR0325sP3aGhNKAxG9ndN8r+OR4GSKNEZGnhRG9u7Hrq7NI\ndCYS7maGdu/CnrJyJDoDMWcLV3brxL6zFcgMJqKOJgZ16cShikoUBjMheyP9Sks4UlmFymjG19RA\n35KOfFVTg9powdvUQM/iYk7X1aLPycFRV0v34hLO1tWgs1hw1NXRrUNHyhtqMVhyaKmtpXOHYqqa\n6jCZLTTW1tKxoIi65kpMVjMN1Q0UF5RQ31yOJcdAXU0zHWydaGg5Q45VT221naL8rjS1nMKaq6W6\nykWhrTt2xzFyrGqqKr3Y8nvhsB8m16qksipAXl5fHC0HyM1RUFkdJM/WH2fTPqxmORU1IfIKB+Ko\n+4LcHDmVdTHyCgfhrPscq1lCRX2c/KKrcNZ+itUopqJRhK34ahyVH2E1iKholmArGYHj/Daseqho\nkZHfeQTOM1uw6hJUOBTkdxuJ4+R7WLVxKt1qbFeMxn78bayqKJU+LbZeYzmx+zm66FXsanJy36I1\nmMyWy/qeWLWnkrX7qgHoYtXwl+m9L1sdzP827acl/ufET54gevc8+Ef35tJSpEtWItIbUtO0b79/\nLZfitM6Qa1+9aDvevR/d8/1+g/8vI37iiScu9zp8Z/n880NP7NpVQ0JqhliInFwpp86HCUX0CKIo\nek2UsooIobgBIRFBp45RVh0lggEhEUaninKmLk5UMCKKhdAqYpxphqjEhCgWRisJc94uEJVZIBJC\nLQlR6RYTl5shGkIlhKjySUkorSTCQZSiIPVBOYLGSjwcQB7z0xhTIdZZSYQCSON+mhMaJIY8YsEA\n0pgfh6BBbsonFgogDntxSfXILTaiQT+ikBefXIcypyDZ6j7gJagyoMkpIBLwkQh4ielN6POLCPt9\nxHxuEnoLBlsRIb+fiMeNYLRgLCgi5PcR8bqRmK2YCzoQ8vsJeVwoc3IxFxQR8PkIuJyorXlYi4oJ\n+Hz4nQ70efnkdeiA3+vF53ZhzLNh61iCz+PF53JgsdkoKi7F5/XjdjrJLbBSVNIRj9uPx+kht9BM\nh5IOeNwBXA4PhcUGiksLcLsDOO0+Cou1dCyx4XYFcTj8FHdUUdopD5criMMZoLhYTmlpDi53EIcj\nSIdCMaUlZlyeME5nmOJCgU4dTbi8YRyuGB1tcUqKDbg8EZyeGB3zopR00OPyRHG4Y3TMDVFSpMPl\njeH0Jig2+ykt1ODyxXD6RBQbvXQqVOPyxXH6BYr1bkrzlDj9CRwBgY5qOyV5CpwBcIbEdJQ30ctm\nosEfxtrhaoymy3tw0sGk5J3Wpmx2X5i+RQasWvm3z3gZo1bL8fsvz2XY3/eILDmIevch/v67ya/w\nHQ4SBw8gjBuPqPWUafv2+9eiVst/fbEf45XlB564WMueP2/ARV//S5E29c3J+En/kWi0F6UcDH6J\n2jIs5YD7C7R5I1L22r9AX5hu4uVp2IWhJN3ky12zC1O3dNM217kd5PRMNwVznP6IvL43pNz81UcU\nDEg3EWs8upWOV6WbtlXvf49OwyelXLHnXbqOujnl8s820+O6dJOysk/fos/YW1L+6uONDLgx3cTt\nyNaNDJmYbnJ2aMt6ht2cbtq2d/MbjLxlVspfvLWW0dPT3rlhDdfPSDdN275+NRNmppu6bXtjFRNn\npf3+2hVMnZNu8rZ59Qqm335Hym+uXMxt89LTr/v/2rvz+Kiqu4/jn1kyWxICgbAE0EC1v9qKrSKl\nPi2uVRQERUBRQCAIRVxRsXWttWrL08cVAavIqiAq7rVqLSpalUURWQ8CSQwhIYGELGTPzPPHHSYz\nYwLBijOJv/frlRd877n35uQkcE/uPfecRfO4YnxjfZYtWszo8SNC+bmFz3JlZuPX/8z8F5mQOTiU\nF89/mcyJje05/+k3mDih8S2FeXPfIvPKM0L56fnvMnFM4/f36YXvkXlF46Rs8xZ/SOYoa1K2QCDA\n/CUfkznylFBesGwNE4ad1Fj+wudkDj2xsfyl9UwYfEJjfm0j4887rjG/uZUJ5/QKfb6lG5M4b+wd\nxNrMFdt5Z3MhAP17pXLn4J8c5ojY0t/8D6/h7X+GZpEFsJ15VmgWWW2//873ceek31lPHbUL75r3\nJrWJOydxP+ZERE4Xkc9F5EsRue5Q+9bVRX6/AziicvTKgJHTQQdsUdND26NevXQ4D5ltjoRDZ2fk\nGAR7gjsqR5Y7ovZ3RJU7XdE5crp0p9t9yJwQlV1u12HKPVE5stwdVe72RJV7XM3mQCCA1xuZPVHZ\n64mcRM3jcUaVHzr7vJHfL6/bEbm/2x65/zfKwzP4XPZmM0CCPT4Gp10cNjB2dVYxu/dXHWJv1Ro4\nBl6AY/ptoRx4/z0a7r+XtvTLZlsWaAgctY+2Iq47JyLiAOYBlwB9gYki0uzMVv1O6UpDrTUIs766\niN49E/DXWzlQX0zvdDv+umCu20dGF/AH9/fX7CWjE6Hj/VVFHNPeT321Nciz4UAhPZLrqa+ycn15\nAem+euqCubasgC7uamoPWINEa0p2k+asoqaiBICq4jw62iupKQ/mvXmk+MupLi8G4EBhLsn15VSX\nWeXle77GW1NKVamVS3fn4K7az4H91v4leTk4D5SE8r7cbOyle6kosXJRzk4C+/dSESzfk72Dun1F\nlAXLC7J2ULO3MJR379xOZVEhpcVWzt3+FeV78tlfbA2izNn+FaUFBZQGc/Y2Q0l+Y/kOs5XC3fmU\n7CsO5q/Yk1dEyT6r/l9t/Yr83GKK91ntY7bsYHduGcXFVvtt25JN7tflFBdb7b9189fk5FRSXGz9\nBrh58y5yvq4Jy3nk5NaHBs1u2pJPTl6A4pJg3rqHnHwbJcFBt5tMIVn5dkpKrQvzxm1F5BS5QnnT\n9mKyizyUlFmDbDft3E9Wsa8xZ5WRXZrM/uBsqxuzy8iqaNeYcyvIPtCBkgpr/1VZRfh6NE6VH0s9\nU32ceqw1JiEAvPKFDqJsC74xi+zLL9Iw5/EY1kip705cP9YRkdOAPxpjzg/mPwAYY/7a1P7bt+cG\nRg68nqqAkxR7gHmvzmDa9BnsK6mlZ3oy9997I9P+8DdKSmvp3jWRP991A9PvfJDi8nq6d07k3juu\nZfo9D1FS0UD3Tj7+dNs13Hrvw+yv9JOe6uOeW6/m9/c9Smm1n/RUL3ffNIXbHniMslroluLmrpum\ncMeMmZTVQtcUN7dfN4m7H5xFRZ2NLu3c/H7qRO55eA6VDTY6JSbw+6sn8qfH5lDld9DJ5+SWyZnc\nN+tJqrHT0ZPAtInjeGDOU9RiJ9WTwHXjxzLjybnU2Zx0cDu55soxPDh3HnUOJykJDqaOHcPDT8+j\nwZlAktPOlNGjeXTBfPzOBJIcDiZdfjkzF84Hlxuf3UbmpaOY88wibAluvA4b40ZcxpPPLiLB68Hp\nDzB25GXMXbIQh8uDCxg94jLmL11MgttDgg0uGzaSRc8txuXxYvMHuGzYCJ593sp2YPjQESx5fhFu\nrwsbDoYPHcmSZfPw+FzYAk6GDR3Fcy88hcfrBL+bi4dewbIXnsDnc+JvcDN0yBheXD4bn89OIJDI\n4EFjeWn5THxeGw2BJAYPHs/y5x8h0WejIdCOwUMmsHzZQyR6A/htKQwaksny5x7C5wnQQAoXXnwV\ny5f8DZ/HT8DRiUEXXcXyZ/6Kz91AwNmJQcN+x/LF9+NLqCfg6sygYVNYvvDPVnZ3ZdDwKSyfdy8+\nZx0BbzcuGHE1y+feg89ZC950LrjsWh56aAxd3G52UsPMe1fgcMTHxGfrd5Vy5yubAHA57Mwb35cU\nb/SdxPigjyVaLhAI0HDX7fjfeDW0rf1fHqDygosPcZQ6lO/jsc6pv3niqF141340pU081on3zskI\nYKAxZlIwjwH6G2OafLwz9so/BjZuTcNms+P31+N0rAHPb0LZ3vAp9nZnhDJV/8HZ6exQDpR9iKv7\nuVZuqKe+6D08vS7AZrPhb6ijdte7JP7kwlCu2fkO7fpcFMpV296iU99LsNlsNNTXsn/DG3T71chQ\n3rvuNXoOGGXluloKVr9M73OuCOVdH7+EXDAWm81GfV0t2Sue58Qh40J52ztLOXlYppVra9nyz2fp\nf+lV2Gw26mpq+OL1ZxhwxeRgrmbNK4s5a+wUbDYbtTXVfPLCQgZmTg3llUvnMWTStaH878VzGfa7\n66xcXc0/Fz3FpVdfj81mo6aqitcXzmX0NTdgs9morqri1flPMuH6aaH8/FNPMGnaTaH8zN9nMmWa\ndf6qqioWPfF3rrlpcigvmPM01988PpirmTt7MdNuGY3NZqOysoq/z1rG9FsvDeZqnpj1ErdOHxrK\nMx97k1tvHtSYZ73NrTecF8w1zHxiBbdeexY2m40DB6p5/MkPmD51QDDXMGv+J0yf3N/KlTXMWriW\n6RP7NuZF65g+7hfBXMvspV9yy6gTsNlsVFTWMuclw80jjg/lJ17bwc0X9bJyVS2v5/TivOGTv89/\nMs0KBALc+PyX7Cyy7iSN7t+TUf16Huao2NDOyZH5xiyyNps1i+w55x76QNWktt45EZHTgUewxjU8\nZYyZebTq8t+I9zW4j+gbmJdfjc1mPamy250cKA+Q5G3MVWU2klLCyqvttAvfv8aO+2B2OKmud+AN\nvnZpdyRQG0ggKTzjCr2WaXckUG93h7LD6SLg9ERkXL7GnODC7k2MyA5fY3YmuEhITIrI7uTkxuxy\n4WnXLpQT3G4SO6SEZQ9J7Ruzy+0hpWP7iNyhU4eInJoWlj0eOqWlhrLb6yUtLHu8Xrp06RiRu3aL\nzOldG8/n9Xrp0a19VG6sv8fjpme3pLByDxk9EsOym2O6uSNyRrorIh/bJSEsu8jo6ghln89NRld7\nWHaR0TnQuL8ngYw0f2TuFJ6dZKTWNR7vSaBXh9rGcreTjHbVoZzkdZG4bT5pc6YTL5YAoWFYa4Mf\ncSot1hVobU4Mfhy0bQRsi1VlWrm7j/5YsViNDQkbKvFbIA9YIyLvGmO2xKRChxDXY06wGi/817ue\nwK7mdu7SOXIVW4+/MCK7GvZEZHdtQUROiM7VkdlZmR+Vd0dke0VeRLaVR+XSXRE5sD83IvuLv47I\n9VG5bl/OIXNNYXYo+/1+qosic+WerIh8IH9nRC7PjywvK4gsL8vfEZH3747MxXmRuSQv8nz7vpEj\n6783L/LrLcrNjSrPizi+MG93RC7anR9VXhCWAxTuLozM+UVh54fC/L0ReU9BVN5THFGfgsLGDLBn\nb+OkdA0NfmorIie1U0qpGPslsN0Yk22MqQOeAy46zDExEe+PdZyAAc4BdgOrgcub6+WtXr0hcP9N\n91NaUcsxvhyu6bOBhzf2o6i+Gz1dOUz96Xoe2dqfooZudHfmMFW+4NHtv2KvP510RxZTjlvHzOxf\ns4/upLODyRmfMWvXAPbae5DesJ1JPdcyO/909jl6kN7wFVd1X8OcPWdS4uxJ1zpDZpfVPFl8NqXu\nnnSuMozr/CnzSn5LqacnaZVbGdvxExaUn0eZ9xg6VmxmdPuPWVQ5kArfsaSWb2ZU8kcsqRvEgaQM\n2u/fwEjvRyxrGERVci9SSjYwzL2SFxlCdbsMkvd9yTD3Sl62D6UmJYPEovUMcX7Aa86LqGvfC2/h\nFwyyv88/3MOo79ALT8EXDGQFb/uG05DaC+fudQz0r+BfycMhtTeOvM84p2EFK5JHQMfe2Hat5cz6\nFaxMGYm9Y2/8uWs4o24FH3W4FGfHH9GQu4Zf177LqtRRODv1pi5nNafVvMuajqNISDuO2pxV9K/6\nF2vTLsWV1ovqnWvoV72CdWmX4E7LoCprLX2rVrK+8xA8nY+lMmsdJ1d+xMYuF+Lp1IOKnev5eeUn\nbO56Pr7O3anYsYE+B1Zhup2LN60b5Ts3cWLFZ2ztcjbetK6U7dxCn8p1bE07A29aF8qztnJi5Xq2\npg3A27EzZVnbOLFmA1tST8OXmkZZznZOqt/ElpT+eFM7Uf71Dvo0GLYkn4q3QypluVmc5N/GlsRT\n8LbvQHleNn3Yzhb3z/G2a09Zfi59HDvZ4joRb3IK5QW76JOQwxb7CXiTUigvymN45534XG3i8a9S\nPxx3+4/6P9pT+s8+ahfez1dNbbb+RzpUIpbiunMCICJnEPl87LEYV0kppZRqdURkOHB+a+icxPuY\nE4wxHwAnx7oeSimlVCt3REMlYinuOydKKaWU+k6sBY4XkQysoRKXAZcf8ogYifcBsUoppZT6Dhhj\n6oFM4GXgM2BePL6pA61gzIlSSimlflj0zolSSiml4op2TpRSSikVV7RzopRSSqm40ube1mkt6wbE\nCxHpCSwCOgNFwAJjzAIRSQYWA72BHcBYY0xF7Goa34LTQq8Fdhljhmj7tZyIJAKzgZMANzAB2Iy2\nX4uIyCSsNnMDHxpjbtSfv+aJyDxgMFBojOkT3NZse4nI9cBVQD1wvTHmo5hU/AemTd05CVs34BKg\nLzBRRE6Iba3iXh0wzRjzM2AE8Ndgm90FfGyMOQn4FLgzhnVsDW7AuqAeHGGu7ddys4EPjDEnY3VQ\ntqLt1yIikgrcDpwL9AN+LCID0fY7lPnA+VHbmmwvEfkp1tstfbGuKwtEpE1dN+NVW2vkVrNuQLww\nxhQYY74I/n0vsAboDgwFFgZ3WwjoGuzNEJEewCBgLnBw6mhtvxYQkRRggDFmHlivOhpjStH2a6kq\nrJ+5FMAL+ID9aPs1yxjzIVAStbm59roIWGqMqTPGZAPbsa4z6ihra52T7kBuWN4V3KZaQESOA36G\n9ZtDF2PMwZUS9wBdYlax+PcwMB0IX85U269legFFIrJARDaKyFMi4kPbr0WMMVXA1UA2UAD8xxiz\nCm2/I9Vce6UTOYOqXlO+J22tc6KTtnxLIpKEdadpWvSzaWNMAG3bJonIhVjPrtfReNckgrbfITmx\nHkcsD/7pBkaG76Dt1zwRSQPmAD8FMoDTgj+TIdp+R6YF7aVt+T1oa52TVrNuQDwRkQSsi8MzxphX\ng5v3iEjXYHk3oDBW9Ytz/wMMFZEsYClwtogsRtuvpXYB+4wxrwfvAizFGg9QoO3XIr8EPjXGbDfG\n7ANeAAagP39Hqrn2ir6m9AhuU0dZW+uchNYNEBEX1roBr8W4TnFNRGzA08AmY8wjYUWvAeOCfx8H\nvPJ91601MMbcbozpaYzpBYwCVhhjxqLt1yLGmAJgu4j0Dw40HAz8G3gdbb+W+BA4VURSRcQNXAC8\ng/78Hanm2us1YJSIuESkF3A8sDoG9fvBaVOvEhtj6kXk4LoBB18ljst1A+LIr4ExwJcisi647Tbg\nz8BiEfmS4Kt1Mapfa3Pwlq+2X8uNw3qdvROwAfg91i9O2n6HYYwpE5H7sP7P8wFvAe9hXUC1/Zog\nIkuBM4COIpIL3E0z/16NMZtFZD7WOjT1wPjgYx91lOnaOkoppZSKK23tsY5SSimlWjntnCillFIq\nrmjnRCmllFJxRTsnSimllIor2jlRSimlVFzRzolSSiml4op2TpRqxUTkHhHxt2C/M0XELyKnh217\nX0TeO7o1VEqpI9emJmFT6gfq205WNOU7rYVSSn1HtHOiVOvX5IKDh2OM2fpdVUBE3MaYmu/qfEqp\nHzbtnCgVIyLyY2AG1uKB7bAWG1sFXG6MaRCRdODBYHkS8AVwhzHm08OcNwl4BGudlVrgTeDVJvZ7\nHwgYY84K25aINZX3QKwFz7YC/2eMeT5sn/HAPOAU4EbgdKAUOFlE+gEPACdjTaeeD7xljLnmCJpG\nKfUDp50TpWLnH0ANcCewDUjH6lDYRKQ98DlQgbXWURlwDfChiJxljPnoMOf9RfC47VgLYD7exH4R\nS8MHF8v8FEjG6qBkYa0QvEREfMaYBVHHL8Na0+UqwBnsFL0NbAZuBnKAY4HTWtAWSikVop0TpWJA\nRNoBvYFMY8zCsKKlwfJbgI7A/xhjdga3vYl14Z+BtWBjU+c9FxgAXGeMmR3c/I6IrGlidxuR41Wu\nA34GnB7W+VkhIicB94vIwqhFz94wxvwh7HP3Adpj3d35IGy/8K9PKaUOS9/WUSoGjDFlwErgNhG5\nSkSOj9rlNOCTgx2T4DF+4DngVBFpbpzJwbsU/4ra/k4LqnUOsAX4REScBz+wlo3vBhwTtf/LUV/T\nBqy7Lf8rIqNFpGcLPqdSSn2Ddk6Uip0JWGNM/gIYEdkhIpODZenA3iaOKQASgC7NnLMbcMAYsy1q\n+9oW1OdY4ASgDmusysGPx7HusBwbtX9+E+e4BMgFZgM5IrJBRC5uwedWSqkQ7ZwoFSPGmGxjzDhj\nTBrWANL/AHNE5DggD/hVE4d1xeo8FDZz2nwgUUQkanu/FlQpF/gYOLWJj35YY2DCfeMVZmPMemPM\nCKAD1l2cXcAzwcdYSinVIjrmRKk4YIxZLyJ3A2OAwVidhLNF5OfGmPUAIuLAGty6OviIpykfB/88\nFzBh289rQTXeA6YDucaYom/xZYQE67dKRGZgvflzJtbjIaWUOiztnCgVA8FBpo9ijSHZAXQCxmHd\nFVkJ7AQmAS+IyB+BcmAq8CNgYnPnNca8KyIrgftEJEDj2zrJzRwSPnblIWAUsEZEXqVx3MpPgN8Y\nYw75eEZELgQmY41FyQF6BOtcRsseKymlFKCdE6ViJR/rAn4T1kW8GvgSuNAYsw5ARPpizXMyA0jE\nmudkgDFmVdh5Il4HDhqM1fG5A2vMyBvAtcBbUftFHGuMqROR04DbgaFYnaADWHOdLG/i2GjbgErg\nLqyxL+XAauBcY8zu5ptCKaUi2QKBbzvztVJKKaXUd08HxCqllFIqrmjnRCmllFJxRTsnSimllIor\n2jlRSimlVFzRzolSSiml4op2TpRSSikVV7RzopRSSqm4op0TpZRSSsWV/we/pXNyeIhr/AAAAABJ\nRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x108be8110>"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Part III - How to select a solver"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Solving the famous Rosenbrock Banana. Global minimum at 1,1 with 0 value. Reference: http://scipy-lectures.github.io/advanced/mathematical_optimization/"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig = plt.figure()\n",
"ax = Axes3D(fig, azim = -128, elev = 43)\n",
"s = .05\n",
"X = np.arange(-2, 2.+s, s)\n",
"Y = np.arange(-1, 3.+s, s)\n",
"X, Y = np.meshgrid(X, Y)\n",
"Z = (1.-X)**2 + 100.*(Y-X*X)**2\n",
"ax.plot_surface(X, Y, Z, rstride = 1, cstride = 1, norm = LogNorm(), cmap = cm.jet)\n",
" \n",
"plt.xlabel(\"x\")\n",
"plt.ylabel(\"y\")\n",
"plt.show()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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rrNNx442/dF2wdlFqvCaNxB0aEAQ2fiT+Ny8grjoScgw6yI0yHi0f1boGufmT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bo67LbYa4ebuGSxSAqzi1jlaTvOYWQZq4c4zkjwgqbyKy3FAk1gF7NEzoCuWGC3eSR5RCioPjrb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s69KFY/780kHzZfhhZ9o/F4nSqn8y7vdQKlAsFn+kfwL2u4b/+lEurXMf0E8Zf1Tt+r9Ycfov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RRLHtxMt+HF9LzGjiAIrP0wyPavarn9JR+uIg35vMKrE+ow6RXue6lAdFzzeZ4f1kOj0jxX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pDLqwkO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\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nTlM91w0Q2PCdwtqvk6hV28Sw+yVqN4BPZjpJPOjBYFCYOltl12b48wcLISG5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\n5X9Rm84sLIFI6QAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x108b18950>"
]
}
],
"prompt_number": 9
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def f(x): return (1 - x[0])**2 + 100*(x[1] - x[0]**2)**2 # The rosenbrock function\n",
"print \"BruteForce:\",optimize.brute(f, ((-1, 2), (-1, 2)))\n",
"print \"anneal:\",optimize.anneal(f, [2, 2]) #simulated annealing\n",
"print \"anneal:\",optimize.anneal(f, [2, 2],maxiter=10000,schedule='boltzmann', learn_rate=0.5,upper=2,lower=-1)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"BruteForce: [ 0.99998188 0.99996297]\n",
"anneal:Warning: Cooled to 174747.925213 at [ -47.50619239 2215.31782985] but this is not the smallest point found."
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" (array([ -17.94360667, 321.7192422 ]), 5)\n",
"anneal:Warning: Maximum number of iterations exceeded."
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" (array([ 1.00676758, 1.01542639]), 3)\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#other optimization solvers\n",
"print optimize.fmin_cg(f, [2, 2]) #Conjugate gradient descent\n",
"print optimize.fmin(f, [2, 2]) #Simplex method: the Nelder-Mead\n",
"print optimize.fmin_powell(f, [2, 2]) #the Powell algorithm: An efficient method for finding the minimum of a function of several variables without calculating derivatives"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Warning: Desired error not necessarily achieved due to precision loss.\n",
" Current function value: 10.321787\n",
" Iterations: 1\n",
" Function evaluations: 40\n",
" Gradient evaluations: 7\n",
"[ 1.3569372 2.16056499]\n",
"Optimization terminated successfully.\n",
" Current function value: 0.000000\n",
" Iterations: 62\n",
" Function evaluations: 119\n",
"[ 0.99998292 0.99996512]\n",
"Optimization terminated successfully.\n",
" Current function value: 0.000000\n",
" Iterations: 12\n",
" Function evaluations: 339\n",
"[ 1. 1.]\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Further Readings:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- [Choosing a solver](http://www.mathworks.com/help/optim/ug/choosing-a-solver.html)\n",
"- [List of python optimization solver libs](https://wiki.python.org/moin/PythonForOperationsResearch)\n",
"- [Powell, gradient descent & dynamic programming](http://informatik.unibas.ch/fileadmin/Lectures/HS2013/CS253/PowellAndDP1.pdf)"
]
}
],
"metadata": {}
}
]
}
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