Consider a diet problem. Given a set of foods `Foods` and a set of nutrients `Nutrients` which is the union of nutrients with minimum requirements `MinRequirements` and nutrients with maximum requirements `MaxRequirements`. Each food `j` has a cost `Cost_{j}` and the amount of each nutrient `i` it contains is `NutrientAmount_{i, j}`. The problem aims to minimize the total cost of buying foods. It is constrained that the total amount of each nutrient `i` with minimum requirements in the foods bought is at least `MinRequirement_{i}` and the total amount of each nutrient `i` with maximum requirements in the foods bought is at most `MaxRequirement_{i}`. How to decide the amount of each food `j` to buy?
