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   "source": [
    "# Chapter 8 - Linear Programming and Game Theory"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:8.2.2 Pg: 238"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "New corner: [ 0.          0.          0.          0.33333333  3.        ]\n",
      "Minimum cost: -9.33333333333\n"
     ]
    }
   ],
   "source": [
    "from scipy.optimize import linprog\n",
    "from numpy import array, transpose\n",
    "A=array([[1, 0 ,1 ,6, 2],[0, 1, 1, 0, 3]])\n",
    "b=transpose(array([8, 9]))\n",
    "c=transpose(array([0, 0, 7 ,-1, -3]))\n",
    "lb=transpose(array([0, 0 ,0 ,0 ,0]))\n",
    "ub=[]\n",
    "ans=linprog(c,A,b)\n",
    "x=ans.x\n",
    "f=ans.fun\n",
    "print 'New corner:',x\n",
    "print 'Minimum cost:',f"
   ]
  }
 ],
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