A zookeeper has a walrus with a nutritional deficiency. She wants to make sure the walrus consumes at least 2200 mg of iron, 2400 mg of vitamin B-1, and 1500 mg of vitamin B-2. One Maxivite pill contains 400 mg of iron, 300 mg of vitamin B-1, and 75 mg of vitamin B-2, and costs $0.07. One Healthovite pill provides 100 mg of iron, 150 mg of vitamin B-1, and 150 mg of vitamin B-2, and costs $0.06. Complete parts (a)-(c) below. (a) What combination of Maxivite and Healthovite pills will meet the walrus's requirement at lowest cost? What is the lowest cost? Set up the linear programming problem. Let m represent the number of Maxivite pills, h represent the number of Healthovite pills, and c represent the total cost in dollars. Minimize c= 0.07m + 0.06h subject to 400m + 100h 2 2200 300m + 150h 2 2400 75m + 150h 2 1500 m20, h 2 0. (Use integers or decimals for any numbers in the expressions. Do not include the $ symbol in your answers.) The best combination of pills that meets the walrus's nutritional requirements is 4 Maxivite pilI(s) and 8 Healthovite pill(s) at the lowest cost of $ 0.76 . (Type integers or decimals.) (b) In the solution for part (a), does the walrus receive more than the minimum amount he needs of any vitamin? If so, which vitamin is it? Select the correct choice below, and if necessary, fill in the answer boxes to complete your choice. O A. The walrus receives mg more iron, mg more vitamin B-1, and mg more vitamin B-2 than he needs. (Type whole numbers.) O B. The walrus does not receive more than the minimum amount he needs of any vitamin.
A zookeeper has a walrus with a nutritional deficiency. She wants to make sure the walrus consumes at least 2200 mg of iron, 2400 mg of vitamin B-1, and 1500 mg of vitamin B-2. One Maxivite pill contains 400 mg of iron, 300 mg of vitamin B-1, and 75 mg of vitamin B-2, and costs $0.07. One Healthovite pill provides 100 mg of iron, 150 mg of vitamin B-1, and 150 mg of vitamin B-2, and costs $0.06. Complete parts (a)-(c) below. (a) What combination of Maxivite and Healthovite pills will meet the walrus's requirement at lowest cost? What is the lowest cost? Set up the linear programming problem. Let m represent the number of Maxivite pills, h represent the number of Healthovite pills, and c represent the total cost in dollars. Minimize c= 0.07m + 0.06h subject to 400m + 100h 2 2200 300m + 150h 2 2400 75m + 150h 2 1500 m20, h 2 0. (Use integers or decimals for any numbers in the expressions. Do not include the $ symbol in your answers.) The best combination of pills that meets the walrus's nutritional requirements is 4 Maxivite pilI(s) and 8 Healthovite pill(s) at the lowest cost of $ 0.76 . (Type integers or decimals.) (b) In the solution for part (a), does the walrus receive more than the minimum amount he needs of any vitamin? If so, which vitamin is it? Select the correct choice below, and if necessary, fill in the answer boxes to complete your choice. O A. The walrus receives mg more iron, mg more vitamin B-1, and mg more vitamin B-2 than he needs. (Type whole numbers.) O B. The walrus does not receive more than the minimum amount he needs of any vitamin.
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.8: Linear Programming
Problem 5SC: If during the following year it is predicted that each comedy skit will generate 30 thousand and...
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Transcribed Image Text:A zookeeper has a walrus with a nutritional deficiency. She wants to make sure the walrus consumes at least 2200 mg of iron, 2400 mg of vitamin B-1, and 1500 mg of
vitamin B-2. One Maxivite pill contains 400 mg of iron, 300 mg of vitamin B-1, and 75 mg of vitamin B-2, and costs $0.07. One Healthovite pill provides 100 mg of iron,
150 mg of vitamin B-1, and 150 mg of vitamin B-2, and costs $0.06. Complete parts (a)-(c) below.
.....
(a) What combination of Maxivite and Healthovite pills will meet the walrus's requirement at lowest cost? What is the lowest cost?
Set up the linear programming problem. Let m represent the number of Maxivite pills, h represent the number of Healthovite pills, and c represent the total cost in
dollars.
Minimize
c= 0.07m + 0.06h
subject to
400m + 100h 2
2200
300m + 150h 2
2400
75m + 150h 2
1500
m20, h 2 0.
(Use integers or decimals for any numbers in the expressions. Do not include the $ symbol in your answers.)
The best combination of pills that meets the walrus's nutritional requirements is 4 Maxivite pill(s) and 8 Healthovite pill(s) at the lowest cost of $ 0.76 .
(Type integers or decimals.)
(b) In the solution for part (a), does the walrus receive more than the minimum amount he needs of any vitamin? If so, which vitamin is it? Select the correct choice
below, and if necessary, fill in the answer boxes to complete your choice.
A. The walrus receives
mg more iron,
mg more vitamin B-1, and
mg more vitamin B-2 than he needs.
(Type whole numbers.)
B. The walrus does not receive more than the minimum amount he needs of any vitamin.
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