CS164 - Linear Programming I

Linear Programming I.ipynb

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   "source": [
    "# Linear Programming I"
   ]
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     "name": "stdout",
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     "text": [
      "status: optimal\n",
      "Optimal value: 24.000\n",
      "Optimal vars: 6.000, 2.000\n"
     ]
    }
   ],
   "source": [
    "import cvxpy as cp\n",
    "\n",
    "x = cp.Variable()\n",
    "y = cp.Variable()\n",
    "\n",
    "constraints = [y - x*2/3 - 2 <= 0,\n",
    "               y + x*2/3 - 6 <= 0,\n",
    "               x >= 0,\n",
    "               y - x*2/3 + 2 >= 0]\n",
    "\n",
    "obj = cp.Maximize(5*x - 3*y)\n",
    "\n",
    "# Form and solve problem.\n",
    "prob = cp.Problem(obj, constraints)\n",
    "prob.solve()\n",
    "\n",
    "print(\"status:\", prob.status)\n",
    "print(f\"Optimal value: {prob.value:.3f}\")\n",
    "print(f\"Optimal vars: {x.value:.3f}, {y.value:.3f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "status: optimal\n",
      "Optimal value: 8000.000\n",
      "Optimal vars: 80.000, 160.000\n"
     ]
    }
   ],
   "source": [
    "x = cp.Variable()\n",
    "y = cp.Variable()\n",
    "\n",
    "constraints = [y + x <= 240,\n",
    "               y + x*2 <= 320,\n",
    "               x >= 0,\n",
    "               y >= 0]\n",
    "\n",
    "obj = cp.Maximize(40*x + 30*y)\n",
    "\n",
    "# Form and solve problem.\n",
    "prob = cp.Problem(obj, constraints)\n",
    "prob.solve()\n",
    "\n",
    "print(\"status:\", prob.status)\n",
    "print(f\"Optimal value: {prob.value:.3f}\")\n",
    "print(f\"Optimal vars: {x.value:.3f}, {y.value:.3f}\")"
   ]
  }
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