Question

A local company employs a varying number of employees each year, based on its needs. The labor costs for the company include a fixed cost of $41,949.00 each year, and $28,826.00 for each person employed for the year. For the next year, the company projects that labor costs will total $1,483,249.00. How many people does the company intend to employ next year?

Answer 1

50 people.


`1483249.00 - 41949.00 = 1441300`

`1441300 / 28826 = 50`

Answer 2

50

Explanation:

Let

• x = number of employees each year

• y = labor costs

The relationship between x and y can be represented through a linear equation.

y = a . x + b

where,

a is the slope

b is the y-intercept

The slope represents the cost per each person employed, that is, a = $28,826.00/person.

Then,

y = ($28,826.00/person) . x + b

Even if no person is hired (x = 0), there is a fixed cost of $41,949.00 (y = $41,949.00).

$41,949.00 = ($28,826.00/person) . 0 + b

b = $41,949.00

The final equation is

y = ($28,826.00/person) . x + $41,949.00

If the company will spend $1,483,249.00 (y = $1,483,249.00.),

$1,483,249.00 = ($28,826.00/person) . x + $41,949.00

1,441,300 = ($28,826.00/person) . x

x = 50 person (50 people)

The company intends to employ 50 people next year.