Solution - WebAssign

When hired at a new job selling electronics, you are given two pay options.

? Option A: Base salary of $20,000 a year with a commission of 12% of your sales

? Option B: Base salary of $26,000 a year with a commission of 3% of your sales

How much electronics would you need to sell for option A to produce a larger income?

Solution

To find the amount of sales for option A to produce a larger income, first find a model for both

options.

? Let A( s) be the salary in dollars produced per year from option A by selling s dollars¡¯

worth of electronics

o Since the salary increases by 12 cents for each additional dollar in sales, A( s) is

o

o

?

a linear function with a rate of change, or slope, of .12

The initial value is the base salary per year or $20,000.

The linear model is A(s) ? .12s ? 20,000

Let B( s) be the salary in dollars produced per year from option B by selling s dollars¡¯

worth of electronics

o Since the salary increases by 3 cents for each additional dollar in sales, B( s) is a

o

o

linear function with rate of change, or slope, of .03

The initial value is the base salary per year or $26,000.

The linear model is B(s) ? .03s ? 26,000

To find the sales needed so that the salary from option A is greater than option B, find the set of

s-values that make the output values from A(s) ? .12s ? 20,000 greater than the output values

from B(s) ? .03s ? 26,000 by solving the inequality A(s) ? B( s) for s.

.12s ? 20, 000 ? .03s ? 26, 000

.09s ? 6000

6000

s?

? 66, 666.67

.09

Therefore, more than $66,666.67 worth of electronics would need to be sold for option A to

produce a larger income than option B.

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