# 3398

breakfast cereals…

DIET PROBLEM. Grant Winfield is a 71-year-old grandfather who likes to mix breakfast cereals together for taste and as a means of getting at least 50% of the recommended daily allowances (RDA) of five different vitamins and minerals. Concerned about his sugar intake, he wishes his mixture to yield the lowest possible amount of sugar. For taste, each of the cereals listed in the following table must make up at least 1 0 % of the total mixture. The table shows the amounts of the vitamins, minerals, and sugar contained in one ounce together with 1 / 2 cup of skim milk.

a. Formulate and solve for the number of ounces in each cereal that should be mixed together in order to minimize total sugar intake while providing at least 50% of the RDA for each of Vitamins A, C, D, B6 , and iron. How much sugar would be consumed in the process?

b. How much total cereal does Grant need to eat to achieve the minimum 50% RDA in all five categories? How much milk does he consume in doing this?

c. Determine the shadow prices for this problem. Interpret the shadow prices and the corresponding ranges of feasibility.

d. If Grant eliminates the restriction that each cereal must account for at least 1 0 % of the mixture, then, by inspection, why wouldn’t any Frosted Bran be included in the mix? Verify this conclusion by deleting these constraints from the original formulation and re-solving.