Mary has a limited food budget, but still wants to make sure her family members meet their daily nutritional requirements. Mary can buy two foods. Food 1 sells for 7 per pound, and each pound contains 3 units of vitamin A and 1 unit of vitamin C. Food 2 sells for 1 per pound, and each pound contains 1 unit of each vitamin. Each day, the family needs at least 12 units of vitamin A and 6 units of vitamin C.
(A) Verify that Mary should purchase 12 units of food 2 each day and thus oversatisfy the vitamin C requirement by 6 units.
(B) Marys husband has put his foot down and demanded that Mary fulfill the familys daily nutritional requirement exactly by obtaining precisely 12 units of vitamin A and 6 units of vitamin C. The optimal solution to the new problem will involve ingesting less vitamin C, but it will be more expensive, why?
(C) Starting with the optimal solution to (B), use the SolverTable add-in to see what happens to the total cost when the vitamin A and vitamin C requirements both vary (independently) from 3 to 18 in 3-unit increments. That is, from a two-way table. Describe the behavior you observe. In particular, are the changes in total cost the
same as you look across each row of the table? Are they the
same as you look across each column of the table?
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