8
QuizMultiple Choice

Systems of Equations and Inequalities — Test

Question 8 • Algebra 2 with Probability

A catering business offers two sizes of baked ziti. Its small ziti dish uses 1 cup of sauce and 1 and 3 fourths cups of cheese. Its large ziti dish uses 2 cups of sauce and 3 cups of cheese. The business has 100 cups of sauce and 400 cups of cheese on hand. It makes 6 dollars profit on their small dishes and 5 dollars profit on their large dishes. It wants to maximize the profit from selling the two sizes of ziti. Let x represent the number of small dishes and y represent the number of large dishes. What are the constraints for the problem?

Answer
A
x plus 7 fourths y is less than or equal to 6 2 x plus 3 y is less than or equal to 5 x is greater than or equal to 0 y is greater than or equal to 0
B
x plus 2 y is less than or equal to 100 7 fourths x plus 3 y is less than or equal to 400 x is greater than or equal to 0 y is greater than or equal to 0
C
x plus 7 fourths y is less than or equal to 100 2 x plus 3 y is less than or equal to 400 x is greater than or equal to 0 y is greater than or equal to 0
D
x plus 7 fourths y is greater than or equal to 6 2 x plus 3 y is greater than or equal to 5 x is less than or equal to 100 x is less than or equal to 400

Explanation

The sauce constraint is x + 2y ≤ 100 because each small dish uses 1 cup of sauce and each large dish uses 2 cups, with 100 cups available. The cheese constraint is (7/4)x + 3y ≤ 400 because the dishes use 1¾ and 3 cups of cheese, respectively. The numbers of dishes cannot be negative, so x ≥ 0 and y ≥ 0. These are the constraints in choice B.

AI-written and checked against the verified answer.

Previous
Next