8
algebra

A concert hall has 500 seats. Tickets are $20 (regular) and $50 (VIP). Goal: at least $15,000 revenue. Which system models this?

A

r+v≤500,20r+50v≥15000,r≥0,v≥0r + v \leq 500, 20r + 50v \geq 15000, r \geq 0, v \geq 0

B

r+v≥500,20r+50v≥15000,r≥0,v≥0r + v \geq 500, 20r + 50v \geq 15000, r \geq 0, v \geq 0

C

r+v≤500,20r+50v≤15000,r≥0,v≥0r + v \leq 500, 20r + 50v \leq 15000, r \geq 0, v \geq 0

D

r+v≤15000,20r+50v≤500,r≥0,v≥0r + v \leq 15000, 20r + 50v \leq 500, r \geq 0, v \geq 0

Correct Answer: A

Choice A is the correct answer. Constraints on quantity and revenue.

  1. Seats: Total tickets cannot exceed capacity →r+v≤500\rightarrow r + v \leq 500
  2. Revenue: Money must be at least 15000 →20r+50v≥15000\rightarrow 20r + 50v \geq 15000

?�� Strategic Tip: Capacity is usually ≤\leq, Revenue goals are usually ≥\geq.

Choice B is incorrect because it implies they must sell more than capacity. Choice C is incorrect because it implies revenue must be less than goal. Choice D is incorrect because it swaps quantity and money.

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Linear Functions Set 77