Question

A lawn care company charges $20 a week and has 120 clients. The owner estimates that for each $2 increase in its fee, the company would lose 5 clients. What fee should the owner charge to receive the maximum revenue?

a) $22
b) $24
c) $26

Answer 1

The lawn care company should increase their fee to $26 per week to achieve the maximum revenue, which would result in $2730 per week given the estimated loss of clients.

Step-by-step explanation:

To calculate the maximum revenue for the lawn care company, we need to determine the price increase that results in the highest overall revenue. Currently, the company charges $20 a week to each of its 120 clients, which gives us a starting revenue of $2400 per week (20 × 120).

If the company increases the fee by $2, they will lose 5 clients. Thus, if they raise the fee to $22, the number of clients will drop to 115. The new revenue is then calculated as $22 × 115, which equals $2530 per week. Increasing the fee again to $24 would decrease the number of clients to 110, resulting in a revenue of $24 × 110, which equals $2640 per week. A further increase to $26 would decrease the number of clients to 105, resulting in a revenue of $26 × 105, equaling $2730 per week.

Considering these calculations, charging a fee of $26 would result in the highest possible revenue of $2730 per week, given the estimated loss of 5 clients for each $2 increase in fee. Therefore, to achieve the maximum revenue, the owner should charge a fee of $26 per week.