Alan wants to bake blueberry muffins and bran muffins for the school bake sale. For a tray of blueberry muffins, Alan uses 1 third cup of oil and 2 eggs. For a tray of bran muffins, Alan uses 1 half cup of oil and 1 egg. Alan has 4 cups of oil and 12 eggs on hand. He sells trays of blueberry muffins for 12 dollars each and trays of bran muffins for 9 dollars each. Alan wants to maximize the money raised at the bake sale. Let x represent the number of trays of blueberry muffins and y represent the number of trays of bran muffins Alan bakes. What are the constraints for the problem?
Answer
A
1 third x plus 2 y is less than or equal to 12 1 half x plus y is less than or equal to 9 x is greater than or equal to 4 y is greater than or equal to 9
B
1 third x plus 2 y is less than or equal to 12 1 half x plus y is less than or equal to 9 x is greater than or equal to 0 y is greater than or equal to 0
C
1 third x plus 1 half y is less than or equal to 4 2 x plus y is less than or equal to 12 x is greater than or equal to 12 y is greater than or equal to 9
D
1 third x plus 1 half y is less than or equal to 4 2 x plus y is less than or equal to 12 x is greater than or equal to 0 y is greater than or equal to 0
Explanation
Each blueberry tray uses 1/3 cup of oil and each bran tray uses 1/2 cup, so the oil constraint is (1/3)x + (1/2)y ≤ 4. The egg constraint is 2x + y ≤ 12 because the trays use 2 and 1 eggs, respectively. Tray counts cannot be negative, so x ≥ 0 and y ≥ 0. These are the constraints in choice D.
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