Solve the problem
-The manufacturer of a CD player has found that the revenue $R$ (in dollars) is $R ( p ) = - 4 p ^ { 2 } + 1560 p$, 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) $\$ 152,100$
B) $\$ 608,400$
C) $\$ 1,216,800$
D) $\$ 304,200$

Question

Quizplus · Accepted Answer

The maximum revenue can be found by completing the square or using the vertex formula for a parabola. The revenue function is a quadratic equation in the form of $R(p) = -4p^2 + 1560p$. The vertex of this parabola, which gives the maximum point, occurs at $p = -\frac{b}{2a}$, where $a = -4$ and $b = 1560$. Thus, $p = -\frac{1560}{2(-4)} = 195$. Substituting $p = 195$ into the revenue function gives the maximum revenue: $R(195) = -4(195)^2 + 1560(195) = 152,100$.

Solve the Problem -The Manufacturer of a CD Player Has RRR

Solve the Problem
-The Manufacturer of a CD Player Has $R$