5
advanced-math

The cost C(x)C(x) of producing xx widgets is C(x)=2x2−40x+500C(x) = 2x^2 - 40x + 500. What production level minimizes cost?

A

10

B

20

C

40

D

5

Correct Answer: A

Choice A is the correct answer. Since a=2a=2 is positive, the parabola opens upward, so the vertex represents a minimum.

  1. x=−b/2ax = -b/2a.
  2. x=−(−40)/(2×2)=40/4=10x = -(-40) / (2 \times 2) = 40 / 4 = 10.

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

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Set 18: Quadratic Equations and Functions 18