Using linear function concepts, it is found that the correct statements are given by:
- The value of 15000 represents the start-up cost.
- The company spends $57,000 to manufacture 2000 headbands.
<h3>What is a linear function?</h3>
A linear function is modeled by:

In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0, and it can also be interpreted as the initial value.
In this problem, the cost of manufacturing H headbands is given by:

The y-intercept is of 15000, which means that the value of 15000 represents the start-up cost.
Manufacturing 2000 headbands, the cost is of:

Hence, the company spends $57,000 to manufacture 2000 headbands.
More can be learned about linear function concepts at brainly.com/question/24808124