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 dollars for a tray of dog bone treats and 7 dollars for a tray of oatmeal treats. Dana wants to maximize her income from selling the dog treats. When writing constraints for the problem, which definition for the variables x and y can be used to determine the maximum?
Answer
A
Let x represent the number of dog bone treats made 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 trays of dog bone treats made and y represent number of trays of oatmeal dog treats made.
D
Let x represent the number of cups of peanut butter used and y represent the number of cups of flour used.
Explanation
To maximize income, the variables should represent the quantities Dana can choose to make and sell: trays of each treat. Let x be the number of trays of dog bone treats and y be the number of trays of oatmeal treats. Then the ingredient limits can be written as 3x + y ≤ 10 for peanut butter and 2x + 4y ≤ 12 for flour, while income is 6x + 7y. Thus, choice C gives suitable variable definitions.
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