6
advanced-math

A theater sells tickets for 30.Forevery30. For every 1 price increase, they lose 10 customers. They currently have 500 customers. Revenue R(x)=(30+x)(500−10x)R(x) = (30 + x)(500 - 10x). What price increase xx maximizes revenue?

A

$10

B

$20

C

$5

D

$15

Correct Answer: A

Choice A is the correct answer.

  1. Find Roots: 30+x=0⇒x=−3030 + x = 0 \Rightarrow x = -30. 500−10x=0⇒x=50500 - 10x = 0 \Rightarrow x = 50.
  2. Find Vertex: The vertex is exactly halfway between the roots.
  3. Midpoint: (−30+50)/2=20/2=10(-30 + 50) / 2 = 20 / 2 = 10.
  4. So a price increase of $10 maximizes revenue.

Choice B is incorrect. Choice C is incorrect. Choice D is incorrect.

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