Solve.
-The manufacturer of a CD player has found that the revenue function for selling $\mathrm { P } C D$ players is $R ( p ) = - 5 p ^ { 2 } + 1560 p$. Find the maximum revenue to the nearest whole dollar.
A) $\$ 121,680$
B) $\$ 973,440$
C) $\$ 486,720$
D) $\$ 243,360$

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 $R(p) = -5p^2 + 1560p$. The vertex of this parabola, where the maximum revenue occurs, is given by $p = -\frac{b}{2a}$, where $a = -5$ and $b = 1560$. Thus, $p = -\frac{1560}{2(-5)} = 156$. Substituting $p = 156$ back into the revenue function gives $R(156) = -5(156)^2 + 1560(156) = 121,680$.

Solve -The Manufacturer of a CD Player Has Found That PCD\mathrm { P } C DPCD

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-The Manufacturer of a CD Player Has Found That $\mathrm { P } C D$