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VETERINARY SCIENCE A veterinarian has been asked to pre-pare a diet for a group of dogs to be used in a nutrition study at the School of Animal Science. It has been stipulated that each serving should be no larger than 8 oz and must contain at least 29 units of Nutrient I and 20 units of Nutrient II. The vet has decided that the diet may be pre-pared from two brands of dog food: Brand A and Brand B. Each ounce of Brand A contains 3 units of Nutrient I and 4 units of Nutrient H. Each ounce of Brand B contains 5 units of Nutrient I and 2 units of Nutrient H. Brand A costs 3 cents/oz and Brand B costs 4 cents/oz. Determine how many ounces of each brand of dog food should be used per serving to meet the given requirements at minimum cost.

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Finite Mathematics for the Manager...

12th Edition
Soo T. Tan
Publisher: Cengage Learning
ISBN: 9781337405782
BuyFind

Finite Mathematics for the Manager...

12th Edition
Soo T. Tan
Publisher: Cengage Learning
ISBN: 9781337405782

Solutions

Chapter
Section
Chapter 4.3, Problem 22E
Textbook Problem

VETERINARY SCIENCE A veterinarian has been asked to pre-pare a diet for a group of dogs to be used in a nutrition study at the School of Animal Science. It has been stipulated that each serving should be no larger than 8 oz and must contain at least 29 units of Nutrient I and 20 units of Nutrient II. The vet has decided that the diet may be pre-pared from two brands of dog food: Brand A and Brand B. Each ounce of Brand A contains 3 units of Nutrient I and 4 units of Nutrient H. Each ounce of Brand B contains 5 units of Nutrient I and 2 units of Nutrient H. Brand A costs 3 cents/oz and Brand B costs 4 cents/oz. Determine how many ounces of each brand of dog food should be used per serving to meet the given requirements at minimum cost.

Expert Solution
To determine

To find:

The quantity of ounces of each brand of dog food should be used in each serving to meet requirements at minimum cost.

Explanation of Solution

Given:

It is given that,

Each serving should be no larger than 8 oz and must contain at least 29 units of Nutrient I and 20 units of Nutrient II.

Each ounce of Brand A contains 3 units of Nutrient I and 4 units of Nutrient H.

Each ounce of Brand B contains 4 units of Nutrient I and 2 units of Nutrient H.

Brand A costs 3 cents/oz and Brand B costs 4 cents/oz.

Approach:

Represent the given conditions in terms of inequalities and plot the graph for inequalities and then consider the boundary conditions of the graph find optimal solution.

Calculations:

Let us consider that x represents the ounces of Brand A and y represents the ounces of brand B.

So, the objective function for minimum cost is,

C=3x+4y

Since it is given that each ounce of Brand A contains 3 units of Nutrient I and 4 units of Nutrient H and Each ounce of Brand B contains 4 units of Nutrient I and 2 units of Nutrient H also Each serving should be no larger than 8 oz and must contain at least 29 units of Nutrient I and 20 units of Nutrient II. We have,

3x+5y294x+2y20x+y8x0,y0

Plot the inequalities on the graph.

Figure (1)

Consider figure (1) the feasible set is,

(2,6),(3,4),(5.5,2.5)

Substitute 2 for x and 6 for y in the objective function.

C=3(2)+4(6)=30

The cost is 30cents with solution (2,6)

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Chapter 4 Solutions

Finite Mathematics for the Managerial, Life, and Social Sciences
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