Question

Owning a small and successful business isn't easy! There is a monthly cost of shipping supplies and

products of $2000. There is also a monthly cost of $1600 for each employee you hire. If you hire x
employees for the year, what is the total cost, C, in dollars, to keep your business running?

Answer 1

`C(x)=24,000+19,200x`

Explanation:

Mathematical Modeling

To model a real-life situation, a mathematical model can be constructed in such a way it accurately represents the variables measured in the system.

This problem requires to build a model for the yearly cost of a small and successful business.

The first data is the fixed monthly cost or the money the owner must pay regardless of the number of employees he hires. This cost includes shipping supplies and products for $2,000. To operate for a full year, the fixed cost is 12*$2,000=$24,000.

The other component of the cost function is the variable cost of x employees. Given each employee costs $1,600 each month, having x employees cost 1,600x each month. For a full year, the variable cost will be

12*1,600x=19,200x.

We finally form the total cost function:

`\boxed{C(x)=24,000+19,200x}`