7

Set 16: Linear Inequalities

Explanation

Answer: A

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

✓ Correct
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

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Match resources to constraints. 1. Land: 2c+1w≤1002c + 1 w \leq 100 2. Labor: 1c+2w≤801c + 2 w \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).

Key Steps:

•

The correct answer is 2c+w≤100,c+2w≤80,c≥0,w≥02c + w \leq 100, c + 2w \leq 80, c \geq 0, w \geq 0

Why others are wrong:
B: Choice B is incorrect and may result from a calculation error.
C: Choice C is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.
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