Chapter 9.2, Problem 31PPE

To determine

The price charged by the company to maximize the revenue.

Answer to Problem 31PPE

The price of phone should be decreased till $50 for maximum revenue.

Explanation of Solution

Given:

Cell phones sold per week = 500

Charges per phone = $75

Calculation:

The expression will be:

  $\begin{array}{l}\text{revenue of company = no of phones sold }\times \text{ price of one phone}\text{.}\\ \text{Therefore,}\\ \text{Revenue = 500}\left(75\right)\\ \text{Revenue = }\$37500\end{array}$

After the change in the phones sold,

  $\begin{array}{l}\text{revenue of company = no of phones sold }\times \text{ price of one phone}\text{.}\\ \text{Therefore,}\\ \text{Revenue = 520}\left(74\right)\\ \text{Revenue = }\$384800\end{array}$

The equation for revenue can be written as:

  $\begin{array}{l}\text{Revenue}=\left(500-20x\right)\left(75-x\right)\\ \text{For maximum revenue,}\\ \left(500-20x\right)\left(75-x\right)=0\\ \text{Therefore,}\\ x=75,x=25\\ \end{array}$

Hence,

  $\begin{array}{l}x=75-25\\ x=50\end{array}$

The price of phone should be decreased till $50 for maximum revenue.