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