Life Sciences
Health Care David Willis takes vitamin pills. Each day he must have at least 480 IU of vitamin A, 5 mg of vitamin B1, and 100 mg of vitamin C. He can choose between pill 1, which contains 240 IU of vitamin A, 1 mg of vitamin B1, and 10 mg of vitamin C, and pill 2, which contains 60 IU of vitamin A, 1 mg of vitamin B1, and 35 mg of vitamin C. Pill 1 costs 15¢, and pill 2 costs 30¢.
(a) How many of each pill should he buy in order to minimize his cost? What is the minimum cost?
(b) For the solution in part (a), David is receiving more than he needs of at least one vitamin. Identify that vitamin, and tell how much surplus he is receiving. Is there any way he can avoid receiving that surplus while still meeting the other constraints and minimizing the cost? Explain.
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