Description of the Diet Problem
The goal of the diet problem is to find an ”optimal” combination of foods that will satisfy all the daily nutritional requirements of an individual. The problem can be formulated as a linear program with an objective and constraints which require that daily nutritional needs be satisfied. We include constraints that regulate the number of calories and amounts of vitamins, minerals, fats, sodium and cholesterol in the diet.
The original mathematical formulation is simple, but you will find out (from Dantzig’s article) by running the simple model, the diet returns is far from optimal. While our nutritional requirements can be met, there is serious concerns for taste and variety. As Dantzig’s diet problem illustrates, we would never drink gallons of vinegar nor include a few boullion cubes in our meals. However, with careful design of the linear/integer program, healthy optimal meals have been created very successfully.
Formulate the diet problem for your own:
• Select a variety of 100 favorite types of food that you would eat. Do not use any fastfood or pre- processed food. Hence, a sandwich will consist of bread and ham, or peanut butter, jelly, etc. If bread is chosen in the solution, then, ham/peanut butter and jelly will also be chosen, etc.
• UsingthenutritioninformationfromUSDepartmentofAgriculturehttps://www.nal.usda.gov/fnic/foodcomp/ to determine the nutritional value and cost (per serving size) of each of the food you select.
• Generate the AMPL data file.
• Select an objective of your choice.
• Formulate a linear/integer program using AMPL so that the feasible solutions give you the food combination that satisfies the daily nutritional needs for a healthy individual.
• Solve the linear program in CPLEX and LINDO and interpret the results.