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, which definition for the variables x and y can be used to determine the maximum?
Answer
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 represent the number of cups of flour used.
D
Let x represent the number of trays of dog bone treats made and y represent number of trays of oatmeal dog treats made.
Explanation
The variables should represent the quantities Dana can choose that determine both resource use and income: the number of trays of each treat. With x as dog bone trays and y as oatmeal trays, peanut butter use is 3x + y and flour use is 2x + 4y, which can be constrained by the 10 and 12 cups available. Her income is then 6x + 7y, so the correct choice is D: x represents dog bone trays and y represents oatmeal trays.
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