Chapter 3, Problem 22RE

22. Sales Commissions Bill has just been offered a sales position for a computer company. His salary would be $\$25,000$ per year plus $1\%$ of his total annual sales.

(a) Find a linear function that relates Bill's annual salary. S, to his total annual sales, x.

(b) If Bill’s total annual sales were $\$1,000,000$, what would be Bill’s salary?

(c) What would Bill have to sell to ear $\$1,000,000$?

(d) Determine the sales required of Bill for his salary to exceed $\$150,000$.

To determine

To calculate:

a. Find a linear function that relates Bill’s annual salary, $S$ to his total annual sales, $x$.

b. What would be Bill’s salary if his total annual sale is $\$1000000$?

c. What would he have to sell to earn $\$100000$?

d. If his salary has to exceed $\$150000$, how much sales is he required to make?

Answer to Problem 22RE

Solution:

a. $S=25000+0.01x$

b. If the total sale made is $\$1000000$, then his salary would be $\$35000$.

c. If Bill can make selling $\$75,00,000$, then his salary would be $\$100000$.

d. If he can make the sale for more than $\$12500000$, then his salary would exceed $\$150000$.

Explanation of Solution

Given:

The salary offered to Bill is $\$25000$ per year plus $\text{1\%}$ of his total annual sales.

Formula used:

Calculation:

a. The linear function of Bill’s annual salary will be

$S=25000+0.01x$

b. When $x=1000000$, we get

$S(1000000)=25000+0.01(1000000)$

$=35000$

c. If $S=100000$, we get

$100000=25000+0.01(x)$

$\Rightarrow x=\frac{100000-25000}{0.01}$

$=75,00,000$

d. For $S>150000$, we have

$25000+0.01(x)>150000$

$\Rightarrow 0.01x>150000-25000$

$\Rightarrow x>\frac{125000}{0.01}$

$\Rightarrow x>125,00,000$