5
algebra

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 (hA+hBh_A + h_B). Which constraints apply?

A

10A+5B≥100,5A+10B≥200,A,B≥010A + 5B \geq 100, 5A + 10B \geq 200, A,B \geq 0

B

10A+5B≤100,5A+10B≤200,A,B≥010A + 5B \leq 100, 5A + 10B \leq 200, A,B \geq 0

C

10A+5B≥200,5A+10B≥100,A,B≥010A + 5B \geq 200, 5A + 10B \geq 100, A,B \geq 0

D

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

Correct Answer: A

Choice A is the correct answer. Production constraints.

  1. Product X: 10A+5B≥10010A + 5B \geq 100
  2. Product Y: 5A+10B≥2005A + 10B \geq 200
  3. Non-negativity: A,B≥0A, 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.

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Linear Functions Set 79