A salesperson makes 3500035000 a year plus 77 commission on

A salesperson makes $35,000$35000 a year plus 7%7% commission on all sales up to (and including) $250,000$250000. If they exceed $250,000$250000 in sales for a calendar year, the salesperson’s commission jumps to 9%9% for all their remaining sales over $250,000$250000. The salesperson’s total salary SS for a given year is based on their total sales xx. Write the piecewise-defined function S(x).

Solution

Let the total sales be x and let the total salary of the salesperson, including commission on sales be S( x ) Then the commission on sales is 7% of x = 0.07x if x 250000.. Then, the total salary of the sales person, inclding commission on sales, is S( x ) = 35000 + 0.07x ...(1) . However, if x > 250000, then  the commission on sales is 9% of x = 0.09x . Then, the total salary of the sales person, inclding commission on sales, is S( x ) = 35000 + 0.09x ...(2) .   Thus, the required piecewise function is S(x) = 35000 + 0.07x . if x 250000 and S( x ) = 35000 + 0.09x if x > 250000.