2-food-optimization.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%run imports.py"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Preprocessing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Read in the food nutrients and recommended daily allowance DataFrames.\n",
    "nutrients_df = pd.read_msgpack('nutrients.msg')\n",
    "rda_df = pd.read_msgpack('rda.msg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true,
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "# Convert all measurements to grams.\n",
    "def to_grams(df):\n",
    "    def col_to_grams(col):\n",
    "        si = re.findall(r'\\(([^A]?)(?:g|J|L|cal|IU)', col.name)\n",
    "        if len(si) != 1:\n",
    "            raise ValueError(f'Bad column format: {si} ({col.name})')\n",
    "        si = si[0]\n",
    "        if not si:\n",
    "            return col\n",
    "        elif si == 'k':\n",
    "            return 1e3 * col\n",
    "        elif si == 'm':\n",
    "            return 1e-3 * col\n",
    "        elif si in ['µ', 'μ']:  # These two mus are different chars.\n",
    "            return 1e-6 * col\n",
    "        else:\n",
    "            raise ValueError(f'Unknown unit: {si} ({col.name})')\n",
    "    for col in df.select_dtypes(exclude=['object']).columns:\n",
    "        df[col] = col_to_grams(df[col])\n",
    "    return df\n",
    "\n",
    "nutrients_df = to_grams(nutrients_df)\n",
    "rda_df = to_grams(rda_df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Remove RDA columns that are not measured in the food nutrients DataFrame.\n",
    "verified_missing = [\n",
    "    # Elements\n",
    "    'Chromium(μg/d)',\n",
    "    'Iodine(μg/d)',\n",
    "    'Molybdenum(μg/d)',\n",
    "    'Chloride(g/d)',\n",
    "    # Vitamins\n",
    "    'Biotin(μg/d)',\n",
    "    # Macronutrients\n",
    "    'Total Watera(L/d)'\n",
    "]\n",
    "rda_df = rda_df.drop(verified_missing, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Rename RDA columns to match the food nutrients column names.\n",
    "exceptions = {\n",
    "    # Elements\n",
    "    # Vitamins\n",
    "    'Vitamin A(μg/d)a': 'Vitamin A, RAE(µg)',\n",
    "    'Vitamin D(μg/d)b,c': 'Vitamin D3 (cholecalciferol)(µg)',\n",
    "    'Vitamin E(mg/d)d': 'Vitamin E (alpha-tocopherol)(mg)',\n",
    "    'Vitamin B6(mg/d)': 'Vitamin B-6(mg)',\n",
    "    'Folate(μg/d)f': 'Folate, DFE(µg)',\n",
    "    'Vitamin B12(μg/d)': 'Vitamin B-12(µg)',\n",
    "    # Macronutrients\n",
    "    'Total Fiber(g/d)': 'Fiber, total dietary(g)',\n",
    "    'Fat(g/d)': 'Total lipid (fat)(g)',\n",
    "    'Linoleic Acid(g/d)': '18:2 n-6 c,c(g)',  # Part of 'Fatty acids, total polyunsaturated(g)'\n",
    "    'α-Linolenic Acid(g/d)': '18:3 n-3 c,c,c (ALA)(g)',  # Part of 'Fatty acids, total polyunsaturated(g)'\n",
    "    'Proteinb(g/d)': 'Protein(g)'\n",
    "}\n",
    "columns = {**exceptions}\n",
    "for col in rda_df.columns:\n",
    "    if col in exceptions:\n",
    "        continue\n",
    "    query = re.findall(r'^([a-z\\s]+)[^a-z]', col.lower())[0]\n",
    "    results = [c for c in nutrients_df.columns if query in c.lower()]\n",
    "    if len(results) != 1:\n",
    "        raise ValueError(f'Found {results} for \"{query}\" in column {col}')\n",
    "    columns[col] = results[0]\n",
    "rda_df = rda_df.rename(columns=columns)\n",
    "assert all([col in nutrients_df.columns for col in rda_df.columns])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# MILP model that optimizes health, time, cost\n",
    "\n",
    "Possible losses:\n",
    "- Time (Preparation): Waste\n",
    "- Time (Shopping): Number of items\n",
    "- Time (Eating): Meal weight\n",
    "- Health: Recommended Dietary Allowances (Adequate Intake)\n",
    "- Money: Cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 288,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Description</th>\n",
       "      <th>Weight(g)</th>\n",
       "      <th>Calcium, Ca(mg)</th>\n",
       "      <th>Copper, Cu(mg)</th>\n",
       "      <th>Iron, Fe(mg)</th>\n",
       "      <th>Magnesium, Mg(mg)</th>\n",
       "      <th>Manganese, Mn(mg)</th>\n",
       "      <th>Phosphorus, P(mg)</th>\n",
       "      <th>Selenium, Se(µg)</th>\n",
       "      <th>Zinc, Zn(mg)</th>\n",
       "      <th>Potassium, K(mg)</th>\n",
       "      <th>Sodium, Na(mg)</th>\n",
       "      <th>Vitamin A, RAE(µg)</th>\n",
       "      <th>Vitamin C, total ascorbic acid(mg)</th>\n",
       "      <th>Vitamin D3 (cholecalciferol)(µg)</th>\n",
       "      <th>Vitamin E (alpha-tocopherol)(mg)</th>\n",
       "      <th>Vitamin K (phylloquinone)(µg)</th>\n",
       "      <th>Thiamin(mg)</th>\n",
       "      <th>Riboflavin(mg)</th>\n",
       "      <th>Niacin(mg)</th>\n",
       "      <th>Vitamin B-6(mg)</th>\n",
       "      <th>Folate, DFE(µg)</th>\n",
       "      <th>Vitamin B-12(µg)</th>\n",
       "      <th>Pantothenic acid(mg)</th>\n",
       "      <th>Choline, total(mg)</th>\n",
       "      <th>Carbohydrate, by difference(g)</th>\n",
       "      <th>Fiber, total dietary(g)</th>\n",
       "      <th>18:2 n-6 c,c(g)</th>\n",
       "      <th>18:3 n-3 c,c,c (ALA)(g)</th>\n",
       "      <th>Protein(g)</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NDB_NO</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>11302</th>\n",
       "      <td>Peas, edible-podded, frozen, unprepared</td>\n",
       "      <td>144.0</td>\n",
       "      <td>0.072</td>\n",
       "      <td>0.121111</td>\n",
       "      <td>0.36000</td>\n",
       "      <td>0.0825</td>\n",
       "      <td>0.146957</td>\n",
       "      <td>0.104286</td>\n",
       "      <td>0.018182</td>\n",
       "      <td>0.053636</td>\n",
       "      <td>0.058723</td>\n",
       "      <td>0.004000</td>\n",
       "      <td>0.011111</td>\n",
       "      <td>0.352222</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.071667</td>\n",
       "      <td>0.110769</td>\n",
       "      <td>0.045000</td>\n",
       "      <td>0.170769</td>\n",
       "      <td>0.1450</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.2074</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.079769</td>\n",
       "      <td>0.118421</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.071964</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18001</th>\n",
       "      <td>Bagels, plain, enriched, with calcium propiona...</td>\n",
       "      <td>99.0</td>\n",
       "      <td>0.217</td>\n",
       "      <td>0.141111</td>\n",
       "      <td>0.44125</td>\n",
       "      <td>0.0725</td>\n",
       "      <td>0.232174</td>\n",
       "      <td>0.140000</td>\n",
       "      <td>0.387273</td>\n",
       "      <td>0.074545</td>\n",
       "      <td>0.022553</td>\n",
       "      <td>0.278667</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.492667</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>0.468333</td>\n",
       "      <td>0.262308</td>\n",
       "      <td>0.279375</td>\n",
       "      <td>0.053077</td>\n",
       "      <td>0.4025</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0806</td>\n",
       "      <td>0.026364</td>\n",
       "      <td>0.398923</td>\n",
       "      <td>0.042105</td>\n",
       "      <td>0.029235</td>\n",
       "      <td>0.015</td>\n",
       "      <td>0.186607</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11284</th>\n",
       "      <td>Onions, dehydrated flakes</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.013</td>\n",
       "      <td>0.023333</td>\n",
       "      <td>0.01000</td>\n",
       "      <td>0.0125</td>\n",
       "      <td>0.030000</td>\n",
       "      <td>0.021429</td>\n",
       "      <td>0.003636</td>\n",
       "      <td>0.008182</td>\n",
       "      <td>0.017234</td>\n",
       "      <td>0.000667</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.042222</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000667</td>\n",
       "      <td>0.001667</td>\n",
       "      <td>0.020833</td>\n",
       "      <td>0.003846</td>\n",
       "      <td>0.003125</td>\n",
       "      <td>0.061538</td>\n",
       "      <td>0.0200</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0138</td>\n",
       "      <td>0.004909</td>\n",
       "      <td>0.032000</td>\n",
       "      <td>0.013158</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.008036</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15190</th>\n",
       "      <td>Fish, burbot, cooked, dry heat</td>\n",
       "      <td>90.0</td>\n",
       "      <td>0.058</td>\n",
       "      <td>0.255556</td>\n",
       "      <td>0.12875</td>\n",
       "      <td>0.0925</td>\n",
       "      <td>0.350870</td>\n",
       "      <td>0.328571</td>\n",
       "      <td>0.265455</td>\n",
       "      <td>0.079091</td>\n",
       "      <td>0.099149</td>\n",
       "      <td>0.074667</td>\n",
       "      <td>0.004444</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.321667</td>\n",
       "      <td>0.119231</td>\n",
       "      <td>0.111000</td>\n",
       "      <td>0.239231</td>\n",
       "      <td>0.0025</td>\n",
       "      <td>0.034583</td>\n",
       "      <td>0.0312</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.397857</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5002</th>\n",
       "      <td>Chicken, broilers or fryers, meat and skin and...</td>\n",
       "      <td>85.0</td>\n",
       "      <td>0.018</td>\n",
       "      <td>0.084444</td>\n",
       "      <td>0.19000</td>\n",
       "      <td>0.0450</td>\n",
       "      <td>0.023478</td>\n",
       "      <td>0.191429</td>\n",
       "      <td>0.314545</td>\n",
       "      <td>0.147273</td>\n",
       "      <td>0.034468</td>\n",
       "      <td>0.160667</td>\n",
       "      <td>0.171111</td>\n",
       "      <td>0.003333</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.080000</td>\n",
       "      <td>0.162308</td>\n",
       "      <td>0.376312</td>\n",
       "      <td>0.209231</td>\n",
       "      <td>0.0800</td>\n",
       "      <td>0.029583</td>\n",
       "      <td>0.1766</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.059077</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.346607</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                              Description  Weight(g)  \\\n",
       "NDB_NO                                                                 \n",
       "11302             Peas, edible-podded, frozen, unprepared      144.0   \n",
       "18001   Bagels, plain, enriched, with calcium propiona...       99.0   \n",
       "11284                           Onions, dehydrated flakes        5.0   \n",
       "15190                      Fish, burbot, cooked, dry heat       90.0   \n",
       "5002    Chicken, broilers or fryers, meat and skin and...       85.0   \n",
       "\n",
       "        Calcium, Ca(mg)  Copper, Cu(mg)  Iron, Fe(mg)  Magnesium, Mg(mg)  \\\n",
       "NDB_NO                                                                     \n",
       "11302             0.072        0.121111       0.36000             0.0825   \n",
       "18001             0.217        0.141111       0.44125             0.0725   \n",
       "11284             0.013        0.023333       0.01000             0.0125   \n",
       "15190             0.058        0.255556       0.12875             0.0925   \n",
       "5002              0.018        0.084444       0.19000             0.0450   \n",
       "\n",
       "        Manganese, Mn(mg)  Phosphorus, P(mg)  Selenium, Se(µg)  Zinc, Zn(mg)  \\\n",
       "NDB_NO                                                                         \n",
       "11302            0.146957           0.104286          0.018182      0.053636   \n",
       "18001            0.232174           0.140000          0.387273      0.074545   \n",
       "11284            0.030000           0.021429          0.003636      0.008182   \n",
       "15190            0.350870           0.328571          0.265455      0.079091   \n",
       "5002             0.023478           0.191429          0.314545      0.147273   \n",
       "\n",
       "        Potassium, K(mg)  Sodium, Na(mg)  Vitamin A, RAE(µg)  \\\n",
       "NDB_NO                                                         \n",
       "11302           0.058723        0.004000            0.011111   \n",
       "18001           0.022553        0.278667            0.000000   \n",
       "11284           0.017234        0.000667            0.000000   \n",
       "15190           0.099149        0.074667            0.004444   \n",
       "5002            0.034468        0.160667            0.171111   \n",
       "\n",
       "        Vitamin C, total ascorbic acid(mg)  Vitamin D3 (cholecalciferol)(µg)  \\\n",
       "NDB_NO                                                                         \n",
       "11302                             0.352222                               0.0   \n",
       "18001                             0.000000                               0.0   \n",
       "11284                             0.042222                               0.0   \n",
       "15190                             0.000000                               0.0   \n",
       "5002                              0.003333                               0.0   \n",
       "\n",
       "        Vitamin E (alpha-tocopherol)(mg)  Vitamin K (phylloquinone)(µg)  \\\n",
       "NDB_NO                                                                    \n",
       "11302                           0.000000                       0.000000   \n",
       "18001                           0.492667                       0.001667   \n",
       "11284                           0.000667                       0.001667   \n",
       "15190                           0.000000                       0.000000   \n",
       "5002                            0.000000                       0.000000   \n",
       "\n",
       "        Thiamin(mg)  Riboflavin(mg)  Niacin(mg)  Vitamin B-6(mg)  \\\n",
       "NDB_NO                                                             \n",
       "11302      0.071667        0.110769    0.045000         0.170769   \n",
       "18001      0.468333        0.262308    0.279375         0.053077   \n",
       "11284      0.020833        0.003846    0.003125         0.061538   \n",
       "15190      0.321667        0.119231    0.111000         0.239231   \n",
       "5002       0.080000        0.162308    0.376312         0.209231   \n",
       "\n",
       "        Folate, DFE(µg)  Vitamin B-12(µg)  Pantothenic acid(mg)  \\\n",
       "NDB_NO                                                            \n",
       "11302            0.1450          0.000000                0.2074   \n",
       "18001            0.4025          0.000000                0.0806   \n",
       "11284            0.0200          0.000000                0.0138   \n",
       "15190            0.0025          0.034583                0.0312   \n",
       "5002             0.0800          0.029583                0.1766   \n",
       "\n",
       "        Choline, total(mg)  Carbohydrate, by difference(g)  \\\n",
       "NDB_NO                                                       \n",
       "11302             0.000000                        0.079769   \n",
       "18001             0.026364                        0.398923   \n",
       "11284             0.004909                        0.032000   \n",
       "15190             0.000000                        0.000000   \n",
       "5002              0.000000                        0.059077   \n",
       "\n",
       "        Fiber, total dietary(g)  18:2 n-6 c,c(g)  18:3 n-3 c,c,c (ALA)(g)  \\\n",
       "NDB_NO                                                                      \n",
       "11302                  0.118421         0.000000                    0.000   \n",
       "18001                  0.042105         0.029235                    0.015   \n",
       "11284                  0.013158         0.000000                    0.000   \n",
       "15190                  0.000000         0.000000                    0.000   \n",
       "5002                   0.000000         0.000000                    0.000   \n",
       "\n",
       "        Protein(g)  \n",
       "NDB_NO              \n",
       "11302     0.071964  \n",
       "18001     0.186607  \n",
       "11284     0.008036  \n",
       "15190     0.397857  \n",
       "5002      0.346607  "
      ]
     },
     "execution_count": 288,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Extract the RDA for the user.\n",
    "me = 'Males: 19–30 y'\n",
    "my_rda = rda_df.loc[me].dropna()\n",
    "# Drop Fluoride because it is very difficult to find in foods.\n",
    "my_rda.drop(['Fluoride, F(µg)'], axis=0, inplace=True)\n",
    "# Keep only the nutrients we will be evaluating on and\n",
    "# normalize the nutrients to (% of RDA) / (household measure).\n",
    "pct_rda_df = nutrients_df.fillna(0.)[['Description', 'Weight(g)'] + my_rda.index.tolist()].copy()\n",
    "pct_rda_df.loc[:, my_rda.index] = pct_rda_df.loc[:, my_rda.index].divide(my_rda, axis=1)\n",
    "pct_rda_df.sample(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 289,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Drop exotic or difficult to find foods.\n",
    "drop = [\n",
    "    4001,   # Fat, beef tallow\n",
    "    10115,  # Pork pancreas\n",
    "    #14016,  # Amandel melk\n",
    "    14054,  # Amandel melk (chocolate)\n",
    "    14019,  # Tequila sunrise\n",
    "    9059,   # Breadfruit\n",
    "    11218,  # Calabash\n",
    "    19873,  # Frozen novelties (orange)\n",
    "    14160,  # White wine duplicate\n",
    "    7014,   # Liver sausage\n",
    "    11237,  # Kanpyo\n",
    "    16509,  # LOMA LINDA Linketts\n",
    "    1096,   # Milk canned with vit D\n",
    "    11163,  # Collards greens\n",
    "    19874,  # Frozen novelties\n",
    "    1127,   # Egg, yolk, raw, frozen, sugared, pasteurized\n",
    "    18992,  # KELLOGG'S, BEANATURAL, Original 3-Bean Chips\n",
    "]\n",
    "pct_rda_df.drop(drop, axis=0, inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 290,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Variables.\n",
    "purchases = pulp.LpVariable.dicts(\n",
    "    'purchases',\n",
    "    indexs=range(len(pct_rda_df)),\n",
    "    lowBound=0,\n",
    "    upBound=1,\n",
    "    cat='Binary')\n",
    "portions = pulp.LpVariable.dicts(\n",
    "    'portions',\n",
    "    indexs=range(len(pct_rda_df)),\n",
    "    lowBound=0,\n",
    "    upBound=50,\n",
    "    cat='Integer')\n",
    "rda_errors = pulp.LpVariable.dicts(\n",
    "    'rda_errors',\n",
    "    indexs=range(len(my_rda)),\n",
    "    lowBound=0,\n",
    "    upBound=2,\n",
    "    cat='Continuous')\n",
    "max_rda_error = pulp.LpVariable(\n",
    "    'max_rda_error',\n",
    "    lowBound=0,\n",
    "    upBound=2,\n",
    "    cat='Continuous')\n",
    "total_weight = pulp.LpVariable(\n",
    "    'total_weight',\n",
    "    lowBound=0,\n",
    "    upBound=2000,\n",
    "    cat='Continuous')\n",
    "\n",
    "# Cost function.\n",
    "rda_vs_weight = 0.9\n",
    "max_foods = 10\n",
    "max_weight_per_food = 200\n",
    "prob = pulp.LpProblem('food', pulp.LpMinimize)\n",
    "prob += rda_vs_weight * max_rda_error + (1 - rda_vs_weight) * total_weight / 1e3\n",
    "#prob += rda_vs_weight * pulp.lpSum(rda_errors) / len(rda_errors) + (1 - rda_vs_weight) * total_weight / 1e3\n",
    "\n",
    "# Constraints:\n",
    "# - Total weight.\n",
    "prob += total_weight >= pulp.lpSum(pct_rda_df.iat[portion, 1] * portions[portion] for portion in portions)\n",
    "# - Max RDA error.\n",
    "for rda_error in rda_errors:\n",
    "    prob += max_rda_error >= rda_errors[rda_error]\n",
    "# - No more than max_weight per food.\n",
    "for portion in portions:\n",
    "    prob += pct_rda_df.iat[portion, 1] * portions[portion] <= max_weight_per_food\n",
    "# - No more than max_foods.\n",
    "prob += pulp.lpSum(purchases[purchase] for purchase in purchases) <= max_foods\n",
    "# - Purchase is binary.\n",
    "for portion, purchase in zip(portions, purchases):\n",
    "    prob += portions[portion] <= 100 * purchases[purchase]\n",
    "# - RDA error is absolute error per nutrient.\n",
    "for rda_error in rda_errors:\n",
    "    raw_error = pulp.lpSum(pct_rda_df.iat[portion, rda_error + 2] * portions[portion] for portion in portions) - 1.\n",
    "    prob += -rda_errors[rda_error] <= raw_error\n",
    "    prob += raw_error <= rda_errors[rda_error]\n",
    "prob.writeLP('food.lp')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 291,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 291,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Med RDA error is 0.18291666499999998\n",
      "Avg RDA error is 0.2044281917142857\n",
      "Max RDA error is 0.326\n",
      "Total weight is 716.3g\n"
     ]
    },
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Description</th>\n",
       "      <th>Weight(g)</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NDB_NO</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1097</th>\n",
       "      <td>Milk, canned, evaporated, nonfat, with added v...</td>\n",
       "      <td>31.90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1130</th>\n",
       "      <td>Egg, whole, cooked, omelet</td>\n",
       "      <td>15.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015</th>\n",
       "      <td>Spices, curry powder</td>\n",
       "      <td>2.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4026</th>\n",
       "      <td>Salad dressing, mayonnaise, soybean and safflo...</td>\n",
       "      <td>13.80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4585</th>\n",
       "      <td>Margarine-like, margarine-butter blend, soybea...</td>\n",
       "      <td>14.10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9216</th>\n",
       "      <td>Orange peel, raw</td>\n",
       "      <td>6.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11192</th>\n",
       "      <td>Cowpeas (blackeyes), immature seeds, cooked, b...</td>\n",
       "      <td>165.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15014</th>\n",
       "      <td>Fish, cisco, smoked</td>\n",
       "      <td>28.35</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15039</th>\n",
       "      <td>Fish, herring, Atlantic, raw</td>\n",
       "      <td>28.35</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19423</th>\n",
       "      <td>Snacks, potato chips, fat-free, made with olestra</td>\n",
       "      <td>28.35</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                              Description  Weight(g)\n",
       "NDB_NO                                                              \n",
       "1097    Milk, canned, evaporated, nonfat, with added v...      31.90\n",
       "1130                           Egg, whole, cooked, omelet      15.00\n",
       "2015                                 Spices, curry powder       2.00\n",
       "4026    Salad dressing, mayonnaise, soybean and safflo...      13.80\n",
       "4585    Margarine-like, margarine-butter blend, soybea...      14.10\n",
       "9216                                     Orange peel, raw       6.00\n",
       "11192   Cowpeas (blackeyes), immature seeds, cooked, b...     165.00\n",
       "15014                                 Fish, cisco, smoked      28.35\n",
       "15039                        Fish, herring, Atlantic, raw      28.35\n",
       "19423   Snacks, potato chips, fat-free, made with olestra      28.35"
      ]
     },
     "execution_count": 291,
     "metadata": {},
     "output_type": "execute_result"
    },
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Weight(g)</th>\n",
       "      <th>Calcium, Ca(mg)</th>\n",
       "      <th>Copper, Cu(mg)</th>\n",
       "      <th>Iron, Fe(mg)</th>\n",
       "      <th>Magnesium, Mg(mg)</th>\n",
       "      <th>Manganese, Mn(mg)</th>\n",
       "      <th>Phosphorus, P(mg)</th>\n",
       "      <th>Selenium, Se(µg)</th>\n",
       "      <th>Zinc, Zn(mg)</th>\n",
       "      <th>Potassium, K(mg)</th>\n",
       "      <th>Sodium, Na(mg)</th>\n",
       "      <th>Vitamin A, RAE(µg)</th>\n",
       "      <th>Vitamin C, total ascorbic acid(mg)</th>\n",
       "      <th>Vitamin D3 (cholecalciferol)(µg)</th>\n",
       "      <th>Vitamin E (alpha-tocopherol)(mg)</th>\n",
       "      <th>Vitamin K (phylloquinone)(µg)</th>\n",
       "      <th>Thiamin(mg)</th>\n",
       "      <th>Riboflavin(mg)</th>\n",
       "      <th>Niacin(mg)</th>\n",
       "      <th>Vitamin B-6(mg)</th>\n",
       "      <th>Folate, DFE(µg)</th>\n",
       "      <th>Vitamin B-12(µg)</th>\n",
       "      <th>Pantothenic acid(mg)</th>\n",
       "      <th>Choline, total(mg)</th>\n",
       "      <th>Carbohydrate, by difference(g)</th>\n",
       "      <th>Fiber, total dietary(g)</th>\n",
       "      <th>18:2 n-6 c,c(g)</th>\n",
       "      <th>18:3 n-3 c,c,c (ALA)(g)</th>\n",
       "      <th>Protein(g)</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NDB_NO</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "    <tr>\n",
       "      <th>1097</th>\n",
       "      <td>63.80</td>\n",
       "      <td>0.186</td>\n",
       "      <td>0.011111</td>\n",
       "      <td>0.02250</td>\n",
       "      <td>0.0450</td>\n",
       "      <td>0.001739</td>\n",
       "      <td>0.177143</td>\n",
       "      <td>0.029091</td>\n",
       "      <td>0.052727</td>\n",
       "      <td>0.045106</td>\n",
       "      <td>0.049333</td>\n",
       "      <td>0.084444</td>\n",
       "      <td>0.008889</td>\n",
       "      <td>0.080000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.023333</td>\n",
       "      <td>0.152308</td>\n",
       "      <td>0.007000</td>\n",
       "      <td>0.027692</td>\n",
       "      <td>0.0150</td>\n",
       "      <td>0.006667</td>\n",
       "      <td>0.0940</td>\n",
       "      <td>0.029091</td>\n",
       "      <td>0.055692</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.086071</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1130</th>\n",
       "      <td>60.00</td>\n",
       "      <td>0.028</td>\n",
       "      <td>0.040000</td>\n",
       "      <td>0.11000</td>\n",
       "      <td>0.0200</td>\n",
       "      <td>0.006957</td>\n",
       "      <td>0.142857</td>\n",
       "      <td>0.283636</td>\n",
       "      <td>0.058182</td>\n",
       "      <td>0.015319</td>\n",
       "      <td>0.061333</td>\n",
       "      <td>0.115556</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.080000</td>\n",
       "      <td>0.050667</td>\n",
       "      <td>0.023333</td>\n",
       "      <td>0.016667</td>\n",
       "      <td>0.178462</td>\n",
       "      <td>0.002500</td>\n",
       "      <td>0.064615</td>\n",
       "      <td>0.0600</td>\n",
       "      <td>0.018333</td>\n",
       "      <td>0.1544</td>\n",
       "      <td>0.269818</td>\n",
       "      <td>0.003077</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.113571</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015</th>\n",
       "      <td>6.00</td>\n",
       "      <td>0.030</td>\n",
       "      <td>0.080000</td>\n",
       "      <td>0.14250</td>\n",
       "      <td>0.0375</td>\n",
       "      <td>0.216522</td>\n",
       "      <td>0.030000</td>\n",
       "      <td>0.043636</td>\n",
       "      <td>0.024545</td>\n",
       "      <td>0.014681</td>\n",
       "      <td>0.002000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.100000</td>\n",
       "      <td>0.050000</td>\n",
       "      <td>0.010000</td>\n",
       "      <td>0.009231</td>\n",
       "      <td>0.012188</td>\n",
       "      <td>0.004615</td>\n",
       "      <td>0.0075</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0126</td>\n",
       "      <td>0.007091</td>\n",
       "      <td>0.025846</td>\n",
       "      <td>0.086842</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.009375</td>\n",
       "      <td>0.015536</td>\n",
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       "    <tr>\n",
       "      <th>4026</th>\n",
       "      <td>27.60</td>\n",
       "      <td>0.004</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.01750</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.011429</td>\n",
       "      <td>0.007273</td>\n",
       "      <td>0.003636</td>\n",
       "      <td>0.002128</td>\n",
       "      <td>0.104000</td>\n",
       "      <td>0.026667</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.405333</td>\n",
       "      <td>0.056667</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000125</td>\n",
       "      <td>0.123077</td>\n",
       "      <td>0.0050</td>\n",
       "      <td>0.003333</td>\n",
       "      <td>0.0164</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.005692</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.005357</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4585</th>\n",
       "      <td>56.40</td>\n",
       "      <td>0.004</td>\n",
       "      <td>0.004444</td>\n",
       "      <td>0.00500</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.001739</td>\n",
       "      <td>0.005714</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.002553</td>\n",
       "      <td>0.269333</td>\n",
       "      <td>0.511111</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.146667</td>\n",
       "      <td>0.406667</td>\n",
       "      <td>0.003333</td>\n",
       "      <td>0.009231</td>\n",
       "      <td>0.000750</td>\n",
       "      <td>0.003077</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0048</td>\n",
       "      <td>0.006545</td>\n",
       "      <td>0.003385</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.692</td>\n",
       "      <td>0.930000</td>\n",
       "      <td>0.002857</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9216</th>\n",
       "      <td>54.00</td>\n",
       "      <td>0.090</td>\n",
       "      <td>0.060000</td>\n",
       "      <td>0.05625</td>\n",
       "      <td>0.0225</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.012857</td>\n",
       "      <td>0.016364</td>\n",
       "      <td>0.008182</td>\n",
       "      <td>0.024894</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.010000</td>\n",
       "      <td>0.820000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.006000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.052500</td>\n",
       "      <td>0.034615</td>\n",
       "      <td>0.030375</td>\n",
       "      <td>0.076154</td>\n",
       "      <td>0.0450</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0522</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.103846</td>\n",
       "      <td>0.142105</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.014464</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11192</th>\n",
       "      <td>165.00</td>\n",
       "      <td>0.211</td>\n",
       "      <td>0.243333</td>\n",
       "      <td>0.23125</td>\n",
       "      <td>0.2150</td>\n",
       "      <td>0.410435</td>\n",
       "      <td>0.120000</td>\n",
       "      <td>0.074545</td>\n",
       "      <td>0.154545</td>\n",
       "      <td>0.146809</td>\n",
       "      <td>0.004667</td>\n",
       "      <td>0.073333</td>\n",
       "      <td>0.040000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.024000</td>\n",
       "      <td>0.365833</td>\n",
       "      <td>0.139167</td>\n",
       "      <td>0.187692</td>\n",
       "      <td>0.144687</td>\n",
       "      <td>0.082308</td>\n",
       "      <td>0.5250</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0508</td>\n",
       "      <td>0.098727</td>\n",
       "      <td>0.257923</td>\n",
       "      <td>0.215789</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.093393</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15014</th>\n",
       "      <td>28.35</td>\n",
       "      <td>0.007</td>\n",
       "      <td>0.067778</td>\n",
       "      <td>0.01750</td>\n",
       "      <td>0.0125</td>\n",
       "      <td>0.002609</td>\n",
       "      <td>0.061429</td>\n",
       "      <td>0.092727</td>\n",
       "      <td>0.008182</td>\n",
       "      <td>0.017660</td>\n",
       "      <td>0.090667</td>\n",
       "      <td>0.088889</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.253333</td>\n",
       "      <td>0.004000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.010833</td>\n",
       "      <td>0.034615</td>\n",
       "      <td>0.040938</td>\n",
       "      <td>0.058462</td>\n",
       "      <td>0.0025</td>\n",
       "      <td>0.050417</td>\n",
       "      <td>0.0174</td>\n",
       "      <td>0.048909</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.082857</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15039</th>\n",
       "      <td>113.40</td>\n",
       "      <td>0.064</td>\n",
       "      <td>0.115556</td>\n",
       "      <td>0.15500</td>\n",
       "      <td>0.0900</td>\n",
       "      <td>0.017391</td>\n",
       "      <td>0.382857</td>\n",
       "      <td>0.749091</td>\n",
       "      <td>0.101818</td>\n",
       "      <td>0.079149</td>\n",
       "      <td>0.069333</td>\n",
       "      <td>0.035556</td>\n",
       "      <td>0.008889</td>\n",
       "      <td>0.320000</td>\n",
       "      <td>0.080000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.086667</td>\n",
       "      <td>0.203077</td>\n",
       "      <td>0.228000</td>\n",
       "      <td>0.264615</td>\n",
       "      <td>0.0300</td>\n",
       "      <td>0.646667</td>\n",
       "      <td>0.1464</td>\n",
       "      <td>0.133818</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.363571</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19423</th>\n",
       "      <td>141.75</td>\n",
       "      <td>0.050</td>\n",
       "      <td>0.694444</td>\n",
       "      <td>0.42500</td>\n",
       "      <td>0.2500</td>\n",
       "      <td>0.473913</td>\n",
       "      <td>0.350000</td>\n",
       "      <td>0.027273</td>\n",
       "      <td>0.450000</td>\n",
       "      <td>0.350000</td>\n",
       "      <td>0.523333</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.444444</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.387500</td>\n",
       "      <td>0.053846</td>\n",
       "      <td>0.387188</td>\n",
       "      <td>0.173077</td>\n",
       "      <td>0.3000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.2780</td>\n",
       "      <td>0.100000</td>\n",
       "      <td>0.708846</td>\n",
       "      <td>0.250000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.195536</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Weight(g)  Calcium, Ca(mg)  Copper, Cu(mg)  Iron, Fe(mg)  \\\n",
       "NDB_NO                                                             \n",
       "1097        63.80            0.186        0.011111       0.02250   \n",
       "1130        60.00            0.028        0.040000       0.11000   \n",
       "2015         6.00            0.030        0.080000       0.14250   \n",
       "4026        27.60            0.004        0.000000       0.01750   \n",
       "4585        56.40            0.004        0.004444       0.00500   \n",
       "9216        54.00            0.090        0.060000       0.05625   \n",
       "11192      165.00            0.211        0.243333       0.23125   \n",
       "15014       28.35            0.007        0.067778       0.01750   \n",
       "15039      113.40            0.064        0.115556       0.15500   \n",
       "19423      141.75            0.050        0.694444       0.42500   \n",
       "\n",
       "        Magnesium, Mg(mg)  Manganese, Mn(mg)  Phosphorus, P(mg)  \\\n",
       "NDB_NO                                                            \n",
       "1097               0.0450           0.001739           0.177143   \n",
       "1130               0.0200           0.006957           0.142857   \n",
       "2015               0.0375           0.216522           0.030000   \n",
       "4026               0.0000           0.000000           0.011429   \n",
       "4585               0.0000           0.001739           0.005714   \n",
       "9216               0.0225           0.000000           0.012857   \n",
       "11192              0.2150           0.410435           0.120000   \n",
       "15014              0.0125           0.002609           0.061429   \n",
       "15039              0.0900           0.017391           0.382857   \n",
       "19423              0.2500           0.473913           0.350000   \n",
       "\n",
       "        Selenium, Se(µg)  Zinc, Zn(mg)  Potassium, K(mg)  Sodium, Na(mg)  \\\n",
       "NDB_NO                                                                     \n",
       "1097            0.029091      0.052727          0.045106        0.049333   \n",
       "1130            0.283636      0.058182          0.015319        0.061333   \n",
       "2015            0.043636      0.024545          0.014681        0.002000   \n",
       "4026            0.007273      0.003636          0.002128        0.104000   \n",
       "4585            0.000000      0.000000          0.002553        0.269333   \n",
       "9216            0.016364      0.008182          0.024894        0.000000   \n",
       "11192           0.074545      0.154545          0.146809        0.004667   \n",
       "15014           0.092727      0.008182          0.017660        0.090667   \n",
       "15039           0.749091      0.101818          0.079149        0.069333   \n",
       "19423           0.027273      0.450000          0.350000        0.523333   \n",
       "\n",
       "        Vitamin A, RAE(µg)  Vitamin C, total ascorbic acid(mg)  \\\n",
       "NDB_NO                                                           \n",
       "1097              0.084444                            0.008889   \n",
       "1130              0.115556                            0.000000   \n",
       "2015              0.000000                            0.000000   \n",
       "4026              0.026667                            0.000000   \n",
       "4585              0.511111                            0.000000   \n",
       "9216              0.010000                            0.820000   \n",
       "11192             0.073333                            0.040000   \n",
       "15014             0.088889                            0.000000   \n",
       "15039             0.035556                            0.008889   \n",
       "19423             0.000000                            0.444444   \n",
       "\n",
       "        Vitamin D3 (cholecalciferol)(µg)  Vitamin E (alpha-tocopherol)(mg)  \\\n",
       "NDB_NO                                                                       \n",
       "1097                            0.080000                          0.000000   \n",
       "1130                            0.080000                          0.050667   \n",
       "2015                            0.000000                          0.100000   \n",
       "4026                            0.000000                          0.405333   \n",
       "4585                            0.000000                          0.146667   \n",
       "9216                            0.000000                          0.006000   \n",
       "11192                           0.000000                          0.024000   \n",
       "15014                           0.253333                          0.004000   \n",
       "15039                           0.320000                          0.080000   \n",
       "19423                           0.000000                          0.000000   \n",
       "\n",
       "        Vitamin K (phylloquinone)(µg)  Thiamin(mg)  Riboflavin(mg)  \\\n",
       "NDB_NO                                                               \n",
       "1097                         0.000000     0.023333        0.152308   \n",
       "1130                         0.023333     0.016667        0.178462   \n",
       "2015                         0.050000     0.010000        0.009231   \n",
       "4026                         0.056667     0.000000        0.000000   \n",
       "4585                         0.406667     0.003333        0.009231   \n",
       "9216                         0.000000     0.052500        0.034615   \n",
       "11192                        0.365833     0.139167        0.187692   \n",
       "15014                        0.000000     0.010833        0.034615   \n",
       "15039                        0.000000     0.086667        0.203077   \n",
       "19423                        0.000000     0.387500        0.053846   \n",
       "\n",
       "        Niacin(mg)  Vitamin B-6(mg)  Folate, DFE(µg)  Vitamin B-12(µg)  \\\n",
       "NDB_NO                                                                   \n",
       "1097      0.007000         0.027692           0.0150          0.006667   \n",
       "1130      0.002500         0.064615           0.0600          0.018333   \n",
       "2015      0.012188         0.004615           0.0075          0.000000   \n",
       "4026      0.000125         0.123077           0.0050          0.003333   \n",
       "4585      0.000750         0.003077           0.0000          0.000000   \n",
       "9216      0.030375         0.076154           0.0450          0.000000   \n",
       "11192     0.144687         0.082308           0.5250          0.000000   \n",
       "15014     0.040938         0.058462           0.0025          0.050417   \n",
       "15039     0.228000         0.264615           0.0300          0.646667   \n",
       "19423     0.387188         0.173077           0.3000          0.000000   \n",
       "\n",
       "        Pantothenic acid(mg)  Choline, total(mg)  \\\n",
       "NDB_NO                                             \n",
       "1097                  0.0940            0.029091   \n",
       "1130                  0.1544            0.269818   \n",
       "2015                  0.0126            0.007091   \n",
       "4026                  0.0164            0.000000   \n",
       "4585                  0.0048            0.006545   \n",
       "9216                  0.0522            0.000000   \n",
       "11192                 0.0508            0.098727   \n",
       "15014                 0.0174            0.048909   \n",
       "15039                 0.1464            0.133818   \n",
       "19423                 0.2780            0.100000   \n",
       "\n",
       "        Carbohydrate, by difference(g)  Fiber, total dietary(g)  \\\n",
       "NDB_NO                                                            \n",
       "1097                          0.055692                 0.000000   \n",
       "1130                          0.003077                 0.000000   \n",
       "2015                          0.025846                 0.086842   \n",
       "4026                          0.005692                 0.000000   \n",
       "4585                          0.003385                 0.000000   \n",
       "9216                          0.103846                 0.142105   \n",
       "11192                         0.257923                 0.215789   \n",
       "15014                         0.000000                 0.000000   \n",
       "15039                         0.000000                 0.000000   \n",
       "19423                         0.708846                 0.250000   \n",
       "\n",
       "        18:2 n-6 c,c(g)  18:3 n-3 c,c,c (ALA)(g)  Protein(g)  \n",
       "NDB_NO                                                        \n",
       "1097              0.000                 0.000000    0.086071  \n",
       "1130              0.000                 0.000000    0.113571  \n",
       "2015              0.000                 0.009375    0.015536  \n",
       "4026              0.000                 0.000000    0.005357  \n",
       "4585              0.692                 0.930000    0.002857  \n",
       "9216              0.000                 0.000000    0.014464  \n",
       "11192             0.000                 0.000000    0.093393  \n",
       "15014             0.000                 0.000000    0.082857  \n",
       "15039             0.000                 0.000000    0.363571  \n",
       "19423             0.000                 0.000000    0.195536  "
      ]
     },
     "execution_count": 291,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Weight(g)                             716.300000\n",
       "Calcium, Ca(mg)                         0.674000\n",
       "Copper, Cu(mg)                          1.316667\n",
       "Iron, Fe(mg)                            1.182500\n",
       "Magnesium, Mg(mg)                       0.692500\n",
       "Manganese, Mn(mg)                       1.131304\n",
       "Phosphorus, P(mg)                       1.294286\n",
       "Selenium, Se(µg)                        1.323636\n",
       "Zinc, Zn(mg)                            0.861818\n",
       "Potassium, K(mg)                        0.698298\n",
       "Sodium, Na(mg)                          1.174000\n",
       "Vitamin A, RAE(µg)                      0.945556\n",
       "Vitamin C, total ascorbic acid(mg)      1.322222\n",
       "Vitamin D3 (cholecalciferol)(µg)        0.733333\n",
       "Vitamin E (alpha-tocopherol)(mg)        0.816667\n",
       "Vitamin K (phylloquinone)(µg)           0.902500\n",
       "Thiamin(mg)                             0.730000\n",
       "Riboflavin(mg)                          0.863077\n",
       "Niacin(mg)                              0.853750\n",
       "Vitamin B-6(mg)                         0.877692\n",
       "Folate, DFE(µg)                         0.990000\n",
       "Vitamin B-12(µg)                        0.725417\n",
       "Pantothenic acid(mg)                    0.827000\n",
       "Choline, total(mg)                      0.694000\n",
       "Carbohydrate, by difference(g)          1.164308\n",
       "Fiber, total dietary(g)                 0.694737\n",
       "18:2 n-6 c,c(g)                         0.692000\n",
       "18:3 n-3 c,c,c (ALA)(g)                 0.939375\n",
       "Protein(g)                              0.973214\n",
       "dtype: float64"
      ]
     },
     "execution_count": 291,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solver = pulp.solvers.COIN_CMD(\n",
    "    maxSeconds=30,\n",
    "    options=['feasibilityPump off', 'probing off', 'knapsack off', 'clique off', 'flowcover off'])\n",
    "prob.solve(solver=solver)\n",
    "\n",
    "print(f'Med RDA error is {np.median([rda_errors[i].value() for i in rda_errors])}')\n",
    "print(f'Avg RDA error is {np.mean([rda_errors[i].value() for i in rda_errors])}')\n",
    "print(f'Max RDA error is {max_rda_error.value()}')\n",
    "print(f'Total weight is {total_weight.value()}g')\n",
    "\n",
    "x = np.array([portions[p].value() for p in portions])\n",
    "pct_rda_df.iloc[:, :2].loc[x > 0]\n",
    "pct_rda_df.iloc[:, 1:].loc[x > 0].multiply(x[x > 0], axis=0)\n",
    "pct_rda_df.iloc[:, 1:].loc[x > 0].multiply(x[x > 0], axis=0).sum(axis=0)"
   ]
  }
 ],
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