Solve the problem.
-The manufacturer of a CD player has found that the revenue $R$ (in dollars) is $R ( p ) = - 5 p ^ { 2 } + 1,460 p$, when the unit price is $p$ dollars. If the manufacturer sets the price $p$ to maximize revenue, what is the maximum revenue to the nearest whole dollar?
A) $\$ 106,580$
B) $\$ 426,320$
C) $\$ 213,160$
D) $\$ 852,640$

Question

Quizplus · Accepted Answer

The revenue function $R(p) = -5p^2 + 1460p$ is a quadratic function that opens downwards. The maximum revenue occurs at the vertex of the parabola. The vertex $p$ is found using $-b/(2a)$ where $a = -5$ and $b = 1460$. Calculating gives $p = 146$. Substituting $p = 146$ back into the revenue function gives the maximum revenue $R(146) = -5(146)^2 + 1460(146) = 106580$.

Solve the Problem RRR (In Dollars) Is R(p)=−5p2+1,460pR ( p ) = - 5 p ^ { 2 } + 1,460 pR(p)=−5p2+1,460p

Solve the Problem $R$ (In Dollars) Is $R ( p ) = - 5 p ^ { 2 } + 1,460 p$