Balanced_Diet_Problem_Complex.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "from pulp import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Read the given nutrition dataset into a Pandas DataFrame object\n",
    "Note we are reading only the first 64 rows with `nrows=64` argument because we just want to read all the nutrients informtion and not the maximum/minimum bounds in the dataset. We will enter those bounds in the optimization problem separately."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_excel(\"diet.xls\",nrows=64)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Show first 5 rows of the dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Foods</th>\n",
       "      <th>Price/ Serving</th>\n",
       "      <th>Serving Size</th>\n",
       "      <th>Calories</th>\n",
       "      <th>Cholesterol mg</th>\n",
       "      <th>Total_Fat g</th>\n",
       "      <th>Sodium mg</th>\n",
       "      <th>Carbohydrates g</th>\n",
       "      <th>Dietary_Fiber g</th>\n",
       "      <th>Protein g</th>\n",
       "      <th>Vit_A IU</th>\n",
       "      <th>Vit_C IU</th>\n",
       "      <th>Calcium mg</th>\n",
       "      <th>Iron mg</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Frozen Broccoli</td>\n",
       "      <td>0.16</td>\n",
       "      <td>10 Oz Pkg</td>\n",
       "      <td>73.8</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.8</td>\n",
       "      <td>68.2</td>\n",
       "      <td>13.6</td>\n",
       "      <td>8.5</td>\n",
       "      <td>8.0</td>\n",
       "      <td>5867.4</td>\n",
       "      <td>160.2</td>\n",
       "      <td>159.0</td>\n",
       "      <td>2.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Carrots,Raw</td>\n",
       "      <td>0.07</td>\n",
       "      <td>1/2 Cup Shredded</td>\n",
       "      <td>23.7</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>19.2</td>\n",
       "      <td>5.6</td>\n",
       "      <td>1.6</td>\n",
       "      <td>0.6</td>\n",
       "      <td>15471.0</td>\n",
       "      <td>5.1</td>\n",
       "      <td>14.9</td>\n",
       "      <td>0.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Celery, Raw</td>\n",
       "      <td>0.04</td>\n",
       "      <td>1 Stalk</td>\n",
       "      <td>6.4</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>34.8</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.7</td>\n",
       "      <td>0.3</td>\n",
       "      <td>53.6</td>\n",
       "      <td>2.8</td>\n",
       "      <td>16.0</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Frozen Corn</td>\n",
       "      <td>0.18</td>\n",
       "      <td>1/2 Cup</td>\n",
       "      <td>72.2</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.6</td>\n",
       "      <td>2.5</td>\n",
       "      <td>17.1</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2.5</td>\n",
       "      <td>106.6</td>\n",
       "      <td>5.2</td>\n",
       "      <td>3.3</td>\n",
       "      <td>0.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Lettuce,Iceberg,Raw</td>\n",
       "      <td>0.02</td>\n",
       "      <td>1 Leaf</td>\n",
       "      <td>2.6</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.8</td>\n",
       "      <td>0.4</td>\n",
       "      <td>0.3</td>\n",
       "      <td>0.2</td>\n",
       "      <td>66.0</td>\n",
       "      <td>0.8</td>\n",
       "      <td>3.8</td>\n",
       "      <td>0.1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 Foods  Price/ Serving      Serving Size  Calories  \\\n",
       "0      Frozen Broccoli            0.16         10 Oz Pkg      73.8   \n",
       "1          Carrots,Raw            0.07  1/2 Cup Shredded      23.7   \n",
       "2          Celery, Raw            0.04           1 Stalk       6.4   \n",
       "3          Frozen Corn            0.18           1/2 Cup      72.2   \n",
       "4  Lettuce,Iceberg,Raw            0.02            1 Leaf       2.6   \n",
       "\n",
       "   Cholesterol mg  Total_Fat g  Sodium mg  Carbohydrates g  Dietary_Fiber g  \\\n",
       "0             0.0          0.8       68.2             13.6              8.5   \n",
       "1             0.0          0.1       19.2              5.6              1.6   \n",
       "2             0.0          0.1       34.8              1.5              0.7   \n",
       "3             0.0          0.6        2.5             17.1              2.0   \n",
       "4             0.0          0.0        1.8              0.4              0.3   \n",
       "\n",
       "   Protein g  Vit_A IU  Vit_C IU  Calcium mg  Iron mg  \n",
       "0        8.0    5867.4     160.2       159.0      2.3  \n",
       "1        0.6   15471.0       5.1        14.9      0.3  \n",
       "2        0.3      53.6       2.8        16.0      0.2  \n",
       "3        2.5     106.6       5.2         3.3      0.3  \n",
       "4        0.2      66.0       0.8         3.8      0.1  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create the `PuLP` problem variable. Since it is a cost minimization problem, we need to use `LpMinimize`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create the 'prob' variable to contain the problem data\n",
    "prob = LpProblem(\"Simple Diet Problem\",LpMinimize)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create a list of food items from the dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Creates a list of the Ingredients\n",
    "food_items = list(df['Foods'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "So, the food items to consdier, are\n",
      "----------------------------------------------------------------------------------------------------\n",
      "Frozen Broccoli, Carrots,Raw, Celery, Raw, Frozen Corn, Lettuce,Iceberg,Raw, Peppers, Sweet, Raw, Potatoes, Baked, Tofu, Roasted Chicken, Spaghetti W/ Sauce, Tomato,Red,Ripe,Raw, Apple,Raw,W/Skin, Banana, Grapes, Kiwifruit,Raw,Fresh, Oranges, Bagels, Wheat Bread, White Bread, Oatmeal Cookies, Apple Pie, Chocolate Chip Cookies, Butter,Regular, Cheddar Cheese, 3.3% Fat,Whole Milk, 2% Lowfat Milk, Skim Milk, Poached Eggs, Scrambled Eggs, Bologna,Turkey, Frankfurter, Beef, Ham,Sliced,Extralean, Kielbasa,Prk, Cap'N Crunch, Cheerios, Corn Flks, Kellogg'S, Raisin Brn, Kellg'S, Rice Krispies, Special K, Oatmeal, Malt-O-Meal,Choc, Pizza W/Pepperoni, Taco, Hamburger W/Toppings, Hotdog, Plain, Couscous, White Rice, Macaroni,Ckd, Peanut Butter, Pork, Sardines in Oil, White Tuna in Water, Popcorn,Air-Popped, Potato Chips,Bbqflvr, Pretzels, Tortilla Chip, Chicknoodl Soup, Splt Pea&Hamsoup, Vegetbeef Soup, Neweng Clamchwd, Tomato Soup, New E Clamchwd,W/Mlk, Crm Mshrm Soup,W/Mlk, Beanbacn Soup,W/Watr, "
     ]
    }
   ],
   "source": [
    "print(\"So, the food items to consdier, are\\n\"+\"-\"*100)\n",
    "for f in food_items:\n",
    "    print(f,end=', ')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create a dictinary of costs for all food items"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "costs = dict(zip(food_items,df['Price/ Serving']))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'2% Lowfat Milk': 0.23,\n",
       " '3.3% Fat,Whole Milk': 0.16,\n",
       " 'Apple Pie': 0.16,\n",
       " 'Apple,Raw,W/Skin': 0.24,\n",
       " 'Bagels': 0.16,\n",
       " 'Banana': 0.15,\n",
       " 'Beanbacn Soup,W/Watr': 0.67,\n",
       " 'Bologna,Turkey': 0.15,\n",
       " 'Butter,Regular': 0.05,\n",
       " \"Cap'N Crunch\": 0.31,\n",
       " 'Carrots,Raw': 0.07,\n",
       " 'Celery, Raw': 0.04,\n",
       " 'Cheddar Cheese': 0.25,\n",
       " 'Cheerios': 0.28,\n",
       " 'Chicknoodl Soup': 0.39,\n",
       " 'Chocolate Chip Cookies': 0.03,\n",
       " \"Corn Flks, Kellogg'S\": 0.28,\n",
       " 'Couscous': 0.39,\n",
       " 'Crm Mshrm Soup,W/Mlk': 0.65,\n",
       " 'Frankfurter, Beef': 0.27,\n",
       " 'Frozen Broccoli': 0.16,\n",
       " 'Frozen Corn': 0.18,\n",
       " 'Grapes': 0.32,\n",
       " 'Ham,Sliced,Extralean': 0.33,\n",
       " 'Hamburger W/Toppings': 0.83,\n",
       " 'Hotdog, Plain': 0.31,\n",
       " 'Kielbasa,Prk': 0.15,\n",
       " 'Kiwifruit,Raw,Fresh': 0.49,\n",
       " 'Lettuce,Iceberg,Raw': 0.02,\n",
       " 'Macaroni,Ckd': 0.17,\n",
       " 'Malt-O-Meal,Choc': 0.52,\n",
       " 'New E Clamchwd,W/Mlk': 0.99,\n",
       " 'Neweng Clamchwd': 0.75,\n",
       " 'Oatmeal': 0.82,\n",
       " 'Oatmeal Cookies': 0.09,\n",
       " 'Oranges': 0.15,\n",
       " 'Peanut Butter': 0.07,\n",
       " 'Peppers, Sweet, Raw': 0.53,\n",
       " 'Pizza W/Pepperoni': 0.44,\n",
       " 'Poached Eggs': 0.08,\n",
       " 'Popcorn,Air-Popped': 0.04,\n",
       " 'Pork': 0.81,\n",
       " 'Potato Chips,Bbqflvr': 0.22,\n",
       " 'Potatoes, Baked': 0.06,\n",
       " 'Pretzels': 0.12,\n",
       " \"Raisin Brn, Kellg'S\": 0.34,\n",
       " 'Rice Krispies': 0.32,\n",
       " 'Roasted Chicken': 0.84,\n",
       " 'Sardines in Oil': 0.45,\n",
       " 'Scrambled Eggs': 0.11,\n",
       " 'Skim Milk': 0.13,\n",
       " 'Spaghetti W/ Sauce': 0.78,\n",
       " 'Special K': 0.38,\n",
       " 'Splt Pea&Hamsoup': 0.67,\n",
       " 'Taco': 0.59,\n",
       " 'Tofu': 0.31,\n",
       " 'Tomato Soup': 0.39,\n",
       " 'Tomato,Red,Ripe,Raw': 0.27,\n",
       " 'Tortilla Chip': 0.19,\n",
       " 'Vegetbeef Soup': 0.71,\n",
       " 'Wheat Bread': 0.05,\n",
       " 'White Bread': 0.06,\n",
       " 'White Rice': 0.08,\n",
       " 'White Tuna in Water': 0.69}"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "costs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create a dictionary of calories for all food items"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "calories = dict(zip(food_items,df['Calories']))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create a dictionary of cholesterol for all food items"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "cholesterol = dict(zip(food_items,df['Cholesterol mg']))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create a dictionary of total fat for all food items"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "fat = dict(zip(food_items,df['Total_Fat g']))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create a dictionary of sodium for all food items"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "sodium = dict(zip(food_items,df['Sodium mg']))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create a dictionary of carbohydrates for all food items"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "carbs = dict(zip(food_items,df['Carbohydrates g']))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create a dictionary of dietary fiber for all food items"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "fiber = dict(zip(food_items,df['Dietary_Fiber g']))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create a dictionary of protein for all food items"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "protein = dict(zip(food_items,df['Protein g']))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create a dictionary of vitamin A for all food items"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "vit_A = dict(zip(food_items,df['Vit_A IU']))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create a dictionary of vitamin C for all food items"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "vit_C = dict(zip(food_items,df['Vit_C IU']))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create a dictionary of calcium for all food items"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "calcium = dict(zip(food_items,df['Calcium mg']))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create a dictionary of iron for all food items"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "iron = dict(zip(food_items,df['Iron mg']))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create a dictionary of food portion with lower bound 0 - these are the main optimization variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# A dictionary called 'food_vars' is created to contain the referenced Variables\n",
    "food_vars = LpVariable.dicts(\"Portion\",food_items,0,cat='Continuous')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create another set of variables for each food, with integer 0 or 1. These are indicator variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "# A dictionary called 'food_vars' is created to contain the referenced Variables\n",
    "food_chosen = LpVariable.dicts(\"Chosen\",food_items,0,1,cat='Integer')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Adding the objective function to the problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The objective function is added to 'prob' first\n",
    "prob += lpSum([costs[i]*food_vars[i] for i in food_items]), \"Total Cost of the balanced diet\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Adding the calorie constraints to the problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "prob += lpSum([calories[f] * food_vars[f] for f in food_items]) >= 1500.0, \"CalorieMinimum\"\n",
    "prob += lpSum([calories[f] * food_vars[f] for f in food_items]) <= 2500.0, \"CalorieMaximum\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Adding other nutrient constraints to the problem one by one..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Cholesterol\n",
    "prob += lpSum([cholesterol[f] * food_vars[f] for f in food_items]) >= 30.0, \"CholesterolMinimum\"\n",
    "prob += lpSum([cholesterol[f] * food_vars[f] for f in food_items]) <= 240.0, \"CholesterolMaximum\"\n",
    "\n",
    "# Fat\n",
    "prob += lpSum([fat[f] * food_vars[f] for f in food_items]) >= 20.0, \"FatMinimum\"\n",
    "prob += lpSum([fat[f] * food_vars[f] for f in food_items]) <= 70.0, \"FatMaximum\"\n",
    "\n",
    "# Sodium\n",
    "prob += lpSum([sodium[f] * food_vars[f] for f in food_items]) >= 800.0, \"SodiumMinimum\"\n",
    "prob += lpSum([sodium[f] * food_vars[f] for f in food_items]) <= 2000.0, \"SodiumMaximum\"\n",
    "\n",
    "# Carbs\n",
    "prob += lpSum([carbs[f] * food_vars[f] for f in food_items]) >= 130.0, \"CarbsMinimum\"\n",
    "prob += lpSum([carbs[f] * food_vars[f] for f in food_items]) <= 450.0, \"CarbsMaximum\"\n",
    "\n",
    "# Fiber\n",
    "prob += lpSum([fiber[f] * food_vars[f] for f in food_items]) >= 125.0, \"FiberMinimum\"\n",
    "prob += lpSum([fiber[f] * food_vars[f] for f in food_items]) <= 250.0, \"FiberMaximum\"\n",
    "\n",
    "# Protein\n",
    "prob += lpSum([protein[f] * food_vars[f] for f in food_items]) >= 60.0, \"ProteinMinimum\"\n",
    "prob += lpSum([protein[f] * food_vars[f] for f in food_items]) <= 100.0, \"ProteinMaximum\"\n",
    "\n",
    "# Vitamin A\n",
    "prob += lpSum([vit_A[f] * food_vars[f] for f in food_items]) >= 1000.0, \"VitaminAMinimum\"\n",
    "prob += lpSum([vit_A[f] * food_vars[f] for f in food_items]) <= 10000.0, \"VitaminAMaximum\"\n",
    "\n",
    "# Vitamin C\n",
    "prob += lpSum([vit_C[f] * food_vars[f] for f in food_items]) >= 400.0, \"VitaminCMinimum\"\n",
    "prob += lpSum([vit_C[f] * food_vars[f] for f in food_items]) <= 5000.0, \"VitaminCMaximum\"\n",
    "\n",
    "# Calcium\n",
    "prob += lpSum([calcium[f] * food_vars[f] for f in food_items]) >= 700.0, \"CalciumMinimum\"\n",
    "prob += lpSum([calcium[f] * food_vars[f] for f in food_items]) <= 1500.0, \"CalciumMaximum\"\n",
    "\n",
    "# Iron\n",
    "prob += lpSum([iron[f] * food_vars[f] for f in food_items]) >= 10.0, \"IronMinimum\"\n",
    "prob += lpSum([iron[f] * food_vars[f] for f in food_items]) <= 40.0, \"IronMaximum\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Adding constraint linking `food_vars` and `food_chosen`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "for f in food_items:\n",
    "    prob += food_vars[f]>= food_chosen[f]*0.1\n",
    "    prob += food_vars[f]<= food_chosen[f]*1e5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Adding constraint of celery and frozen broccoli"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "prob += food_chosen['Frozen Broccoli']+food_chosen['Celery, Raw']<=1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Adding constraint of at least 3 types of meat/poultry/fish/eggs in every diet"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "protein_choices = ['Beanbacn Soup,W/Watr','Bologna,Turkey','Frankfurter, Beef','Ham,Sliced,Extralean',\n",
    "                  'Hamburger W/Toppings','Hotdog, Plain','Kielbasa,Prk','Neweng Clamchwd','Pizza W/Pepperoni',\n",
    "                  'Poached Eggs','Pork','Roasted Chicken','Sardines in Oil','Scrambled Eggs','Vegetbeef Soup',\n",
    "                   'White Tuna in Water']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "prob += lpSum([food_chosen[p] for p in protein_choices]) >= 3.0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Writing problem data to a `.lp` file"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The problem data is written to an .lp file\n",
    "prob.writeLP(\"SimpleDietProblem.lp\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Run the solver"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The problem is solved using PuLP's choice of Solver\n",
    "prob.solve()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Print the problem solution status `'optimal'`, `'infeasible'`, `'unbounded'` etc..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Status: Optimal\n"
     ]
    }
   ],
   "source": [
    "# The status of the solution is printed to the screen\n",
    "print(\"Status:\", LpStatus[prob.status])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Scan through the problem variables and print out only if the variable quanity is positive i.e. it is included in the optimal solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The optimal (least cost) balanced diet with additional constraints (e.g. at least 3 types of animal protein sources, consists of\n",
      "--------------------------------------------------------------------------------------------------------------\n",
      "Portion_Celery,_Raw = 42.399358\n",
      "Portion_Kielbasa,Prk = 0.1\n",
      "Portion_Lettuce,Iceberg,Raw = 82.802586\n",
      "Portion_Oranges = 3.0771841\n",
      "Portion_Peanut_Butter = 1.9429716\n",
      "Portion_Poached_Eggs = 0.1\n",
      "Portion_Popcorn,Air_Popped = 13.223294\n",
      "Portion_Scrambled_Eggs = 0.1\n"
     ]
    }
   ],
   "source": [
    "print(\"The optimal (least cost) balanced diet with additional constraints \\\n",
    "(e.g. at least 3 types of animal protein sources, consists of\\n\"+\"-\"*110)\n",
    "for v in prob.variables():\n",
    "    if v.varValue>0 and v.name[0]=='P':\n",
    "        print(v.name, \"=\", v.varValue)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Print the optimal diet cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The total cost of this balanced diet is: $4.51\n"
     ]
    }
   ],
   "source": [
    "print(\"The total cost of this balanced diet is: ${}\".format(round(value(prob.objective),2)))"
   ]
  }
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