Solve the problem.
-The manufacturer of a CD player has found that the revenue $R$ (in dollars) is $R ( p ) = - 5 p ^ { 2 } + 1850 p$, 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) $\$ 171,125$
B) $\$ 342,250$
C) $\$ 684,500$
D) $\$ 1,369,000$

Question

Quizplus · Accepted Answer

To find the maximum revenue, we first need to find the vertex of the parabola represented by the revenue function $R(p) = -5p^2 + 1850p$. The vertex form of a parabola is given by $-\frac{b}{2a}$ for the $p$-coordinate, where $a = -5$ and $b = 1850$. Calculating this gives $p = -\frac{1850}{2(-5)} = 185$. Substituting $p = 185$ back into the revenue function gives $R(185) = -5(185)^2 + 1850(185) = 171125$, which rounds to \$171,125.

Solve the Problem RRR (In Dollars) Is R(p)=−5p2+1850pR ( p ) = - 5 p ^ { 2 } + 1850 pR(p)=−5p2+1850p

Solve the Problem $R$ (In Dollars) Is $R ( p ) = - 5 p ^ { 2 } + 1850 p$