a. How many of each pill should he buy in order to minimize his​ cost? What is the minimum​ cost?   He should buy 22 of pill 1 and 11 of pill 2. The minimum cost is $11. ​(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.   He is receiving:   ___ IU of vitamin​ A, : ___mg of vitamin B1​, and ___mg of vitamin C more than he needs. ​(Simplify your​ answers.)

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter5: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 11P
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Question
A patient takes vitamin pills. Each day he must have at least
300 IU of vitamin​ A, 3 mg of vitamin B1​, and 60 mg of vitamin C. He can choose between pill​ 1, which contains 180 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 40 mg of vitamin C. Pill 1 costs 25¢​, and pill 2 costs 50¢.
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 22 of pill 1 and 11 of pill 2. The minimum cost is $11.
​(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.
 
He is receiving:   ___ IU of vitamin​ A, : ___mg of vitamin B1​,
and ___mg of vitamin C more than he needs.
​(Simplify your​ answers.)
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