Question

A salesman is paid $450 a week, plus a commission of 35 cents for every item that he sells. Write a linear function where the paycheck, P, of the salesman is a function of the number, N, of items he sells. If the salesman only has 1400 items available to sell each week, find the domain and range of the function.

Answer 1

The domain is thus [0, 1400].

The range is thus [$450, $940]

Explanation:

A suitable function is P(N) = ($450) + ($0.35 / item)*N, where $450 is the base pay per week and N is the number of items sold.

In this case the salesman has only 1400 items available to sell each week. Therefore N begins at 0 (no items to sell) and ends at 1400 (the max number of items available to sell). The domain is thus [0, 1400].

The smallest amount the salesman could receive would be when he has not sold any items: $450.

The max amount is then $450 + ($0.35/item)(1400 items), or

$450 + $490, or

$940

The range is thus [$450, $940]

Answer 2

Explanation:

1400×0.35

490+450

940