{"id":149,"date":"2021-01-19T21:31:25","date_gmt":"2021-01-19T21:31:25","guid":{"rendered":"https:\/\/www.kindsonthegenius.com\/data-science\/?p=149"},"modified":"2021-01-20T12:23:02","modified_gmt":"2021-01-20T12:23:02","slug":"the-stigler-diet-linear-programming-problem-in-python","status":"publish","type":"post","link":"https:\/\/www.kindsonthegenius.com\/data-science\/the-stigler-diet-linear-programming-problem-in-python\/","title":{"rendered":"The Stigler Diet Linear Programming Problem in Python"},"content":{"rendered":"

The Stigler Diet<\/a> problem is similar to the diet problem we solved previously<\/a>. The difference is that we now have much more data to work with.<\/p>\n

The objective is to determine how many dollar to be spend of each foodstuff at a minimum white satisfying the minimum nutrition requirement. The table below provides the list of foodstuff(commodity) along with their cost per unit and the nutrient content.<\/p>\n

For example, Macaroni cost 14.1 cents and contains 418g of Protein, 0.7g of Calcium etc.<\/p>\n\n\n\n\n\n\n\n\n
Commodity<\/td>\nUnits<\/td>\nPrice (cents)<\/td>\nCalories<\/td>\nProtein (g)<\/td>\nCalcium (g)<\/td>\nIron(mg)<\/td>\nvitamin A(IU)<\/td>\nThiamine (mg)<\/td>\nRiboflavin (mg)<\/td>\nNiacin (mg)<\/td>\nAscorbic Acid (mg)<\/td>\n<\/tr>\n<\/thead>\n
Wheat Flour<\/td>\n10 lb.<\/td>\n36<\/td>\n44.7<\/td>\n1411<\/td>\n2<\/td>\n365<\/td>\n0<\/td>\n55.4<\/td>\n33.3<\/td>\n441<\/td>\n0<\/td>\n<\/tr>\n
Macaroni<\/td>\n1 lb.<\/td>\n14.1<\/td>\n11.6<\/td>\n418<\/td>\n0.7<\/td>\n54<\/td>\n0<\/td>\n3.2<\/td>\n1.9<\/td>\n68<\/td>\n0<\/td>\n<\/tr>\n
…<\/td>\n…<\/td>\n…<\/td>\n…<\/td>\n…<\/td>\n…<\/td>\n…<\/td>\n…<\/td>\n…<\/td>\n…<\/td>\n…<\/td>\n…<\/td>\n<\/tr>\n
Strawberry Preserves<\/td>\n1 lb.<\/td>\n20.5<\/td>\n6.4<\/td>\n11<\/td>\n0.4<\/td>\n7<\/td>\n0.2<\/td>\n0.2<\/td>\n0.4<\/td>\n3<\/td>\n0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

We are also provided with the minimum daily requirements for the 8 nutrients. This is as given in the table below:<\/p>\n

 <\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Nutrient<\/b><\/td>\nMinimum daily requirement<\/b><\/td>\n<\/tr>\n<\/thead>\n
Calories<\/td>\n3,000 Calories<\/td>\n<\/tr>\n
Protein<\/td>\n70 grams<\/td>\n<\/tr>\n
Calcium<\/td>\n.8 grams<\/td>\n<\/tr>\n
Iron<\/td>\n12 mg<\/td>\n<\/tr>\n
Vitamin A<\/td>\n5,000 IU<\/td>\n<\/tr>\n
Thiamine (Vitamin B1)<\/td>\n1.8 mg<\/td>\n<\/tr>\n
Riboflavin (Vitamin B2)<\/td>\n2.7 mg<\/td>\n<\/tr>\n
Niacin<\/td>\n18 mg<\/td>\n<\/tr>\n
Ascorbic Acid (Vitamin C)<\/td>\n75 mg<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Since the nutrients have all been normalized by the price, the goal is now to minimize the sum of the foods, therefore,<\/p>\n