The profit (in dollars) obtained from producing and selling units of a certain item…

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

The profit (in dollars) obtained from producing and selling

x

units of a certain item is modeled by

P(x)=100x-2x^{2}-5e^{-0.1x}, \quad x\ge 0.

Using a graphing calculator or numerical methods, which production level is closest to the number of units that maximizes profit? (a)

15

(b)

50

(c)

25

(d)

35