Diet problem
A canteen has to plan the composition of the meals that it provides. A meal can be composed of the types of food indicated in the following table. Costs, in Euro per hg, and availabilities, in hg, are also indicated.
Food Cost Availability
Bread 0.1 4
Milk 0.5 3
Eggs 0.12 1
Meat 0.9 2
Cake 1.3 2
A meal must contain at least the following amount of each nutrient
Nutrient Minimal quantity
Calories 600 cal
Proteins 50 g
Calcium 0.7 g
Each hg of each type of food contains to following amount of nutrients
Food Calories Proteins Calcium
Bread 30 cal 5 g 0.02 g
Milk 50 cal 15 g 0.15 g
Eggs 150 cal 30 g 0.05 g
Meat 180 cal 90 g 0.08 g
Cake 400 cal 70 g 0.01 g
Give a linear programming formulation for the problem of finding a diet (a meal) of minimum total cost which satisfies the minimum nutrient requirements.
Document prepared by L. Liberti, S. Bosio, S. Coniglio and C. Iuliano. 1
