Question

Big Red Motors, Inc., employs 15 personnel to market its line of luxury automobiles. The average car sells for $75,000, and a 6 percent commission is paid to the salesperson. Big Red Motors is considering a change to the commission arrangement where the company would pay each salesperson a salary of $1,600 per mont plus a commission of 2 percent of the sales made by that salesperson. What is the amount of total monthly car sales at whit Big Red Motors would be indifferent as to which plan to select?

Answer 1

Answer: $600,000

Explanation:

The commission earned per car in the initial arrangement is:

= 6% * Total cars sales

With the second arrangement the amount spent would be:

= Salary of employees + commission

= (15 * 1,600) + (2% * total car sales)

= 24,000 + (2% * car sales)

Assuming total car sales is x, relevant expression is:

6% * x = 24,000 + (2% * x)

0.06x = 24,000 + 0.02x

0.06x - 0.02x = 24,000

0.04x = 24,000

x = 24,000 / 0.04

x = $600,000