A patient takes vitamin pills. Each day he must have at least 180 IU of vitamin A, 4 mg of vitamin B1, and 70 mg of vitamin C. He can choose between pill 1, which contains 90 IU of vitamin A, 1 mg of vitamin B1, and 10 mg of vitamin C, and pill 2, which contains 30 IU of vitamin A, 1 mg of vitamin B1, and 25 mg of vitamin C. Pill 1 costs 15¢, and pill 2 costs 45¢. Complete parts a and b below. Question content area bottom

Part 1

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, the patient is receiving more than he needs of at least one vitamin.

Identify that vitamin, and tell how much surplus he is receiving.