3
advanced-math

Profit P(x)P(x) from selling xx items is P(x)=−x2+200x−1000P(x) = -x^2 + 200x - 1000. How many items must be sold to maximize profit?

A

100

B

200

C

50

D

1000

Correct Answer: A

Choice A is the correct answer. Find the x-coordinate of the vertex.

  1. x=−b/2ax = -b/2a.
  2. x=−200/(2(−1))=−200/−2=100x = -200 / (2(-1)) = -200 / -2 = 100.
  3. Selling 100 items maximizes profit.

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

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Set 18: Quadratic Equations and Functions 18