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Finite Mathematics for the Managerial, Life, and Social SciencesVETERINARY 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.BuyFind*arrow_forward*

12th Edition

Soo T. Tan

Publisher: Cengage Learning

ISBN: 9781337405782

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.

**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

Each ounce of Brand

Brand

**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

So, the objective function for minimum cost is,

Since it is given that each ounce of Brand

Plot the inequalities on the graph.

Figure

Consider figure

Substitute

The cost is

Finite Mathematics for the Managerial, Life, and Social Sciences

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