JJ Motors, Inc., employs 45 sales personnel to market its line of luxury automobiles. The average car sells for $23,000, and a 6% commission is paid to the salesperson. JJ Motors is considering a change to a commission arrangement that would pay each salesperson a salary of $2,000 per month plus a commission of 2% of the sales made by that salesperson. The amount of total monthly car sales at which JJ Motors would be indifferent as to which plan to select is

Answer (A) is correct. Given that X equals the cars sold, the indifference equation and its solution are as follows: ($23,000 × 6%)X = ($23,000 × 2%)X + (45 × $2,000)
$920X = 90,000
X = 97.8261 Cars
At a price of $23,000 each, 97.8261 cars will sell for $2,250,000. Another approach is to determine the sales per person at which $2,000 is equal to a 4% commission. This amount is $50,000 ($2,000 ÷ .04) per person, or $2,250,000 (45 × $50,000) for the entire sales force.