The minimum cost is ​$________.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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A patient takes vitamin pills. Each day he must have at least 540 IU of vitamin​ A, 35 mg of vitamin B​, and 80 mg of vitamin C. He can choose between pill​ 1, which contains 180 IU of vitamin​ A, 5 mg of vitamin B ​, and 10 mg of vitamin​ C, and pill​ 2, which contains 60 IU of vitamin​ A, 5 mg of vitamin ​, and 20 mg of vitamin C. Pill 1 costs 30 cent ​, and pill 2 costs 15 cent . 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 ​$________.

 

 


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.  
He is receiving

____ IU of vitamin A, 

_____ mg of vitamin B,

______ mg of vitamin c more than he needs

 

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