A veterinarian has been asked to prepare 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 prepared 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 II. Each ounce of brand B contains 5 units of nutrient I and 2 units of nutrient II. Brand A costs 5 cents/ounce and brand B costs 9 cents/ounce. Determine how many ounces of each brand of dog food should be used per serving to meet the given requirements at a minimum cost.
A) 5.5 ounces of brand A and 2.5 ounces of brand B
B) 2 ounces of brand A and 6 ounces of brand B
C) 2 ounces of brand A and 4 ounces of brand B
D) 3 ounces of brand A and 4 ounces of brand B

Question

Quizplus · Accepted Answer

To minimize cost while meeting nutrient requirements, we set up equations based on the given information. For nutrient I: $3A + 5B \geq 29$ and for nutrient II: $4A + 2B \geq 20$, where A and B are ounces of brands A and B, respectively. The cost function to minimize is $5A + 9B$. Solving these equations with the constraints $A + B \leq 8$ and minimizing cost leads to the solution of 5.5 ounces of brand A and 2.5 ounces of brand B.

A Veterinarian Has Been Asked to Prepare a Diet for a Group