A patient takes vitamin pills. Each day he must have at least 900 IU of vitamin A, 14 mg of vitamin B₁, and 80 mg of vitamin C. He can choose between pill 1, which contains 180 IU of vitamin A, 2 mg of vitamin B₁, and 10 mg of vitamin C, and pill 2, which contains 90 IU of vitamin A, 2 mg of vitamin B₁, and 15 mg of vitamin C. Pill 1 costs 25¢, and pill 2 costs 75¢. Complete parts a and b below. a. How many of each pill should he buy in order to minimize his cost? What is the minimum cost? He should buy 8 of pill 1 and 0 of pill 2. The minimum cost is $ 2. (Simplify your answers. Type integers or decimals.) 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. mg of vitamin B₁, and mg of vitamin C more than he needs. He is receiving IU of vitamin A, (Simplify your answers.)
A patient takes vitamin pills. Each day he must have at least 900 IU of vitamin A, 14 mg of vitamin B₁, and 80 mg of vitamin C. He can choose between pill 1, which contains 180 IU of vitamin A, 2 mg of vitamin B₁, and 10 mg of vitamin C, and pill 2, which contains 90 IU of vitamin A, 2 mg of vitamin B₁, and 15 mg of vitamin C. Pill 1 costs 25¢, and pill 2 costs 75¢. Complete parts a and b below. a. How many of each pill should he buy in order to minimize his cost? What is the minimum cost? He should buy 8 of pill 1 and 0 of pill 2. The minimum cost is $ 2. (Simplify your answers. Type integers or decimals.) 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. mg of vitamin B₁, and mg of vitamin C more than he needs. He is receiving IU of vitamin A, (Simplify your answers.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A patient takes vitamin pills. Each day he must have at least 900 IU of vitamin A, 14 mg of vitamin B₁, and 80
mg of vitamin C. He can choose between pill 1, which contains 180 IU of vitamin A, 2 mg of vitamin B₁, and 10
mg of vitamin C, and pill 2, which contains 90 IU of vitamin A, 2 mg of vitamin B₁, and 15 mg of vitamin C. Pill 1
costs 25¢, and pill 2 costs 75¢. Complete parts a and b below.
a. How many of each pill should he buy in order to minimize his cost? What is the minimum cost?
He should buy 8 of pill 1 and 0 of pill 2. The minimum cost is $ 2.
(Simplify your answers. Type integers or decimals.)
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.
mg of vitamin C more than he needs.
and
He is receiving IU of vitamin A, mg of vitamin B₁, a
(Simplify your answers.)
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