{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "The optimal value is 9.79\n",
      "The values for variable x are: [[1.5       ]\n",
      " [4.28571429]\n",
      " [4.        ]]\n"
     ]
    }
   ],
   "source": [
    "import cvxpy as cp\n",
    "import numpy as np\n",
    "# inputs\n",
    "A = np.array([[10, 0, 0],              \n",
    "              [0, 7, 0],              \n",
    "              [0, 0, 5]])\n",
    "\n",
    "c = np.ones((3,1))\n",
    "b = np.array([15, 30, 20]).reshape((3,1))\n",
    "# declaring variables\n",
    "x = cp.Variable((3,1))\n",
    "\n",
    "# defining objective\n",
    "objective = cp.Minimize(cp.sum(x))\n",
    "\n",
    "# defining constraints\n",
    "constraints = [A@x==b,\n",
    "              x>=0]\n",
    "\n",
    "myprob = cp.Problem(objective, constraints)\n",
    "myprob.solve()\n",
    "# printing outputs\n",
    "print(\"\\nThe optimal value is\", round(myprob.value, 2))\n",
    "print(\"The values for variable x are:\", myprob.variables()[0].value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[15],\n",
       "       [30],\n",
       "       [20]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def calculate_reduced_costs(c, B):\n",
    "    #Get inverse of basis matrix\n",
    "    B_inv = np.linalg.inv(B)\n",
    "    #Get reduced costs for simplex method step\n",
    "    w = B_inv.dot(c)\n",
    "    #Return index of minimum value\n",
    "    return np.argmin(w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "The optimal value is 11.0\n",
      "The values for variable x are: [[11.]\n",
      " [ 0.]\n",
      " [ 0.]]\n"
     ]
    }
   ],
   "source": [
    "#Knapsack problem\n",
    "a= cp.Variable((3,1), integer=True)\n",
    "w = np.array([7, 11, 16]).reshape((3,1))\n",
    "\n",
    "knapsack_objective = cp.Maximize(cp.sum(a))\n",
    "# defining constraints\n",
    "knap_sack_constraints = [cp.sum(cp.multiply(w,a))<=80,\n",
    "              a>=0]\n",
    "knapsack_prob = cp.Problem(knapsack_objective, knap_sack_constraints)\n",
    "knapsack_prob.solve()\n",
    "\n",
    "# printing outputs\n",
    "print(\"\\nThe optimal value is\", round(knapsack_prob.value, 2))\n",
    "print(\"The values for variable x are:\", knapsack_prob.variables()[0].value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "For I,j,k in range(0, int(W/min(w)):\n",
    "If each I j and k times their weight <= b(each element associated with which entry I j and k weights are multiplied by):\n",
    "Append to an empty list [i, j, k]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "cannot unpack non-iterable int object",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-52-63e51660b59f>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[0mW\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m80\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[1;32mfor\u001b[0m \u001b[0mi\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mj\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mk\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mW\u001b[0m\u001b[1;33m/\u001b[0m\u001b[0mmin\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mw\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      3\u001b[0m                 \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mj\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mk\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mTypeError\u001b[0m: cannot unpack non-iterable int object"
     ]
    }
   ],
   "source": [
    "W=80\n",
    "for i,j,k in range(0, int(W/min(w))):\n",
    "                print(i,j,k)"
   ]
  }
 ],
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