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Linear Programming — Quiz

Question 1 • Advanced Financial Algebra

A café makes waffles and pancakes. Each waffle takes 3 minutes to cook, and each pancake takes 2 minutes to cook. The café has 30 minutes available for cooking each morning. The café must make a non-negative number of waffles and pancakes. Which system of inequalities best models the cooking time constraint and non-negative requirements on the number of waffles ( x ) and pancakes ( y ) the café can make?

Answer
A
3⁢x+2⁢y≥30, x is equal to 0, y is equal to 0
B
2⁢x+3⁢y≤30, x≥0, y≥0
C
3⁢x+2⁢y≤30, x≥0, y≥0
D
3⁢x+2⁢y≥30, x≥0, y≥0

Explanation

Each waffle uses 3 minutes, so x waffles take 3x minutes; each pancake uses 2 minutes, so y pancakes take 2y minutes. The total cooking time cannot exceed 30 minutes, giving 3x + 2y ≤ 30. Since the café cannot make a negative number of either food, x ≥ 0 and y ≥ 0, which matches choice C.

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