A patient takes vitamin pills. Each day he must have at least 360 IU of vitamin A, 4 mg of vitamin B₁, and 140 mg of vitamin C. He can choose between pill 1, which contains 180 IU of vitamin A, 1 mg of vitamin B₁, and 20 mg of vitamin C, and pill 2, which contains 60 IU of vitamin A, 1 mg of vitamin B₁, and 50 mg of vitamin C. Pill 1 costs 10¢, and pill 2 costs 5¢. 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 of pill 1 and of pill 2. The minimum cost is $ (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. He is receiving IU of vitamin A, mg of vitamin B₁, and (Simplify your answers.) Is there any way he can avoid receiving that surplus while still meeting the other constraints and minimizing cost? Explain. Choose the correct answer below. OA. No. Reducing the surplus would either cause the cost to increase or cause the patient to receive less than needed of another vitamin. OB. Yes. Take one fewer of each pill to reduce the cost. OC. Yes. Reverse the numbers of each pill taken.
A patient takes vitamin pills. Each day he must have at least 360 IU of vitamin A, 4 mg of vitamin B₁, and 140 mg of vitamin C. He can choose between pill 1, which contains 180 IU of vitamin A, 1 mg of vitamin B₁, and 20 mg of vitamin C, and pill 2, which contains 60 IU of vitamin A, 1 mg of vitamin B₁, and 50 mg of vitamin C. Pill 1 costs 10¢, and pill 2 costs 5¢. 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 of pill 1 and of pill 2. The minimum cost is $ (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. He is receiving IU of vitamin A, mg of vitamin B₁, and (Simplify your answers.) Is there any way he can avoid receiving that surplus while still meeting the other constraints and minimizing cost? Explain. Choose the correct answer below. OA. No. Reducing the surplus would either cause the cost to increase or cause the patient to receive less than needed of another vitamin. OB. Yes. Take one fewer of each pill to reduce the cost. OC. Yes. Reverse the numbers of each pill taken.
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Transcribed Image Text:A patient takes vitamin pills. Each day he must have at least 360 IU of vitamin A, 4 mg of vitamin B₁, and 140 mg of
vitamin C. He can choose between pill 1, which contains 180 IU of vitamin A, 1 mg of vitamin B₁, and 20 mg of vitamin
C, and pill 2, which contains 60 IU of vitamin A, 1 mg of vitamin B₁, and 50 mg of vitamin C. Pill 1 costs 10¢, and pill 2
costs 5¢ 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 of pill 1 and of pill 2. The minimum cost is $
(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.
He is receiving IU of vitamin A, mg of vitamin B₁, and
(Simplify your answers)
Is there any way he can avoid receiving that surplus while still meeting the other constraints and minimizing cost?
Explain. Choose the correct answer below.
OA. No. Reducing the surplus would either cause the cost to increase or cause the patient to receive less than
needed of another vitamin.
B. Yes. Take one fewer of each pill to reduce the cost
OC. Yes. Reverse the numbers of each pill taken.
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