Q.69 - Intermediate Algebra

Question

A manufacturer of stereo sound speakers has found that the revenue received from selling the speakers at a cost of $p$ dollars each is given by the polynomial function $R\left(p\right) =-4p^2 + 420p$.

Find the revenue received when $p=60$ dollars.

Step-by-Step Solution

Answer

The revenue received when $p=60$ dollars is $10800$.

Step 1. Given Information

A manufacturer of stereo sound speakers has found that the revenue received from selling the speakers at a cost of $p$ dollars each is given by the polynomial function $R\left(p\right) =-4p^2 + 420p$.

We find the revenue received when $p=60$ dollars.

Step 2. The given polynomial function is R ( p )   = − 4 p 2   +   420 p .

The function is $R\left(p\right) =-4p^2 + 420p$

putting $p=60$

$$\begin{gathered} R\left(60\right) =-4{\left(60\right)}^2 + 420\times 60 \\ R\left(60\right) =-4\times 3600 + 420\times 60 \\ R\left(60\right) =-14400 + 25200 \\ R\left(60\right) =10800 \end{gathered}$$