Question

Dana wants to make two types of dog treats. She has 10 cups of peanut butter and 12 cups of flour. Her dog bone treat recipe uses 3 cups of peanut butter and 2 cups of flour to make one tray. A tray of her oatmeal dog treat recipe uses 1 cup of peanut butter and 4 cups of flour. She plans to sell trays of dog treats at the town festival and charge $6 for a tray of dog bone treats and $7 for a tray of oatmeal treats. Dana wants to maximize her income from selling the dog treats.

When writing constraints for the problem, what is the most reasonable definition for the variables x and y?

A) Let x represent the number of cups of peanut butter used and y represent the number of cups of flour used.

B) Let x represent the number of cups of peanut butter used and y represent the number of trays of dog bone treats made.

C) Let x represent the number of dog bone treats made and y represents the number of cups of flour used.

D) Let x represent the number of trays of dog bone treats made and y represent the number of trays of oatmeal dog treats made.

Answer 1

Answer with explanation:

Number of cups of peanut that Dana has =10 cups

Number of cups of flour that Dana has =12 cups

Let x represent the number of trays of dog bone treats made and y represent the number of trays of oatmeal dog treats made.

Constraints

⇒x>0, y>0

⇒3 x+y ≤10

⇒2 x+4 y ≤ 12

Maximize(Objective Function):

Z=6 x +7 y

⇒⇒ The most reasonable definition for the variables x and y as Dana wants to maximize her income from selling the dog treats

Option D: Let x represent the number of trays of dog bone treats made and y represent the number of trays of oatmeal dog treats made.

Answer 2

D. Let x represent the number of trays of dog bone treats made and y represent number of trays of oatmeal dog treats made.