4: Imagine you are a college student trying to live on a small budget. You want to

minimize your food costs, but you know a diet consisting solely of instant ramen and beer

may be harmful to your health. You look up recommended dietary allowance of several

different nutrients to determine what you should eat to be healthy. Let i = 1...m denote

the nutrients and let bi, i = 1...m denote the minimum daily requirement for each of the

nutrients. Suppose make a list of your n favorite foods. Let j denote their index on your

list and c; be the cost of the jh item. Let a denote the amount of the įth nutrient

contained in the jth item on your food list.

a: Formulate a linear problem to minimize your costs while still getting all of your

daily required nutrients

b: Formulate the dual to this problem

c: Introduce another person to this story who is naturally interested in solving the

dual problem. (Hint: Give semantic meaning to the dual problem)

d: Name some real-world considerations that your model leaves out