3
algebra

A farmer plants corn (cc) and wheat (ww). Corn requires 2 acres, wheat 1 acre. Total land is 100 acres. Labor: Corn 1 hr, Wheat 2 hrs. Total labor 80 hrs. Which system models this?

A

2c+w≤100,c+2w≤80,c≥0,w≥02c + w \leq 100, c + 2w \leq 80, c \geq 0, w \geq 0

B

c+2w≤100,2c+w≤80,c≥0,w≥0c + 2w \leq 100, 2c + w \leq 80, c \geq 0, w \geq 0

C

2c+w≥100,c+2w≥80,c≥0,w≥02c + w \geq 100, c + 2w \geq 80, c \geq 0, w \geq 0

D

2c+w≤80,c+2w≤100,c≥0,w≥02c + w \leq 80, c + 2w \leq 100, c \geq 0, w \geq 0

Correct Answer: A

Choice A is the correct answer. Match resources to constraints.

  1. Land: 2c+1w≤1002c + 1w \leq 100
  2. Labor: 1c+2w≤801c + 2w \leq 80
  3. Non-negativity: c,w≥0c, w \geq 0

?�� Strategic Tip: Label your equations "Land" and "Labor" to avoid swapping them.

Choice B is incorrect because it swaps the coefficients. Choice C is incorrect because it uses ≥\geq (requires more than available). Choice D is incorrect because it swaps the limits (100 and 80).

Next
Question 4 →
Back to Set
Linear Functions Set 77