Set 17: Linear Inequalities (Advanced)

Explanation

Answer: A

A company needs at least 100 units of X and 200 units of Y. Machine A produces 10X and 5Y per hour. Machine B produces 5X and 10Y per hour. Minimize hours ( $h_A + h_B$ ). Which constraints apply?

$10A + 5B \geq 100, 5A + 10B \geq 200, A,B \geq 0$

✓ Correct

$10A + 5B \leq 100, 5A + 10B \leq 200, A,B \geq 0$

$10A + 5B \geq 200, 5A + 10B \geq 100, A,B \geq 0$

$A + B \geq 300, A,B \geq 0$

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Production constraints. 1. Product X: $10A + 5 B \geq 100$ 2. Product Y: $5A + 10 B \geq 200$ 3. Non-negativity: $A, B \geq 0$ Strategic Tip: Ensure the coefficients match the machine output rates for each product. Choice B is incorrect because it sets maximum limits instead of minimum requirements. Choice C is incorrect because it swaps the requirements for X and Y. Choice D is incorrect because it sums the units directly.

Key Steps:

•

The correct answer is $10A + 5B \geq 100, 5A + 10B \geq 200, A,B \geq 0$

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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