Solve the problem.
-The owner of a video store has determined that the profits $\mathrm { P }$ of the store are approximately given by $P ( x ) = - x ^ { 2 } + 150 x + 71$, where $x$ is the number of videos rented daily. Find the maximum profit to the nearest dollar.
A) $\$ 5696$
B) $\$ 5625$
C) $\$ 11,321$
D) $\$ 11,250$

Question

Quizplus · Accepted Answer

The maximum profit occurs at the vertex of the parabola, which is at $x = \frac{-b}{2a} = \frac{-150}{2(-1)} = 75$. The profit at this point is $P(75) = -75^2 + 150(75) + 71 = 5625$.

Solve the Problem P\mathrm { P }P Of the Store Are Approximately Given By

Solve the Problem $\mathrm { P }$ Of the Store Are Approximately Given By