Solve the problem.
-The owner of a video store has determined that the profits $\mathrm { P }$ of the store are approximately given by $P ( x ) = - x ^ { 2 } + 120 x + 67$, where $x$ is the number of videos rented daily. Find the maximum profit to the nearest dollar.
A) \$3667
B) $\$ 3600$
C) $\$ 7267$
D) $\$ 7200$

Question

Quizplus · Accepted Answer

The maximum profit occurs at the vertex of the parabola given by the quadratic function. The vertex $x$ value is $-b/2a$. Here, $a = -1$ and $b = 120$, so $x = 60$. Substituting $x = 60$ into the profit function gives $P(60) = -60^2 + 120 \times 60 + 67 = 3667$.

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