CPM Homework Help : PC3 Problem 6-60

A sales department currently has $30$ salespeople who each average $$50,000$ in monthly sales. A study commissioned by the department manager concludes that for each additional salesperson hired, the average monthly sales per salesperson will decrease by $$1,000$ . Determine the maximum revenue if the department hires the optimal number of salespeople.

Hint:

$\text{number of salespeople}\cdot \frac{\text{average monthly sales}}{\text{salesperson}}=\text{revenue}$

Step 1:

Let $x =$ number of additional salespeople hired.
Write an expression for the total number of salespeople.

Step 2:

Write an expression for the average monthly sales per salesperson if $x$ additional salespeople are hired.

Step 3:

The product of the expressions from Step 1 and Step 2 is the revenue.
This expression should be a quadratic expression that has a maximum value.
What is the maximum value? (Hint: Use a graph.)