Question

the function $f(x) = \frac{600 + 2x}{x}$ yields the average cost in dollars for a company to produce $x$ calendars. which statement best fits the situation modeled by the function?

the company spends $600 on a new computer and printer before beginning the project.

the company will sell the calendars for $2.00 each.

the company expects to sell 600 calendars each month.

the company takes 600 photos before selecting which ones to use for its calendars.

Explanation:

Step1: Analyze the cost function

The average cost function is \( f(x)=\frac{600 + 2x}{x}\), which can be split into \(\frac{600}{x}+\frac{2x}{x}= \frac{600}{x}+ 2\).

Step2: Interpret the terms

• The term \(2\) is a constant cost per calendar (variable cost), and \(\frac{600}{x}\) represents a fixed cost divided by the number of calendars \(x\). The fixed cost here is \(600\) dollars, which is a one - time cost before production starts (like buying a computer and printer).
• The statement "The company will sell the calendars for $2.00 each" is about revenue, not cost, so it's incorrect.
• "The company expects to sell 600 calendars each month" is about sales volume, not related to the cost function's structure.
• "The company takes 600 photos before selecting which ones to use for its calendars" is not related to cost (the function is about average cost of producing calendars).

Answer:

The company spends $600 on a new computer and printer before beginning the project.