Question

Joanna sells insurance. She is given two salary options:

Option 1: Base salary of $12,000 and a 18.5% commission on her sales.
Option 2: Base salary of $8,000 and a 22.4% commission on her sales.
For what range of sales should she choose option 1?
For what range of sales should she choose option 2?

Answer 1

Joanna should choose Option 1 for sales up to $102,564.10 and Option 2 for sales higher than that. This is determined by equating the two salary options and solving for the sales amount.

Step-by-step explanation:

To determine for what range of sales Joanna should choose each salary option, we have to set up two equations representing her total earnings for each option and find the point at which her earnings would be the same. That will divide the sales into two ranges, one in which Option 1 is better and the other in which Option 2 is better.

Earnings for Option 1: Option 1 Earnings = $12,000 + 0.185 × Sales

Earnings for Option 2: Option 2 Earnings = $8,000 + 0.224 × Sales

To find the sales amount where both options yield the same earnings, we set the earnings equations equal to each other and solve for Sales.

$12,000 + 0.185 × Sales = $8,000 + 0.224 × Sales

$12,000 - $8,000 = 0.224 × Sales - 0.185 × Sales

$4,000 = 0.039 × Sales

Sales = $4,000 / 0.039

Sales = $102,564.10

Therefore, Joanna should choose Option 1 for sales up to $102,564.10, and Option 2 for any sales amount above that.