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?\
\bigcirc the company spends $600 on a new computer and printer before beginning the project.\
\bigcirc the company takes 600 photos before selecting which ones to use for its calendars.\
\bigcirc the company expects to sell 600 calendars each month.\
\bigcirc the company will sell the calendars for $2.00 each.

Explanation:

The function \( f(x)=\frac{600 + 2x}{x} \) can be rewritten as \( f(x)=\frac{600}{x}+2 \). In the context of average cost, the term \( \frac{600}{x} \) represents a fixed cost (since it doesn't depend on the number of units \( x \) linearly) and \( 2 \) represents a variable cost per unit. A fixed cost is an expense that doesn't change with the number of units produced, like buying equipment (a new computer and printer) before starting production.

• The second option about taking 600 photos is not related to cost structure.
• The third option about selling 600 calendars monthly is about revenue/sales volume, not cost.
• The fourth option about selling price is about revenue per unit, not cost.

The first option about spending $600 on equipment (a fixed cost) before the project fits the fixed cost component (\( \frac{600}{x} \)) in the average cost function.

Answer:

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