Question

the function $f(x) = \frac{80,000 + 0.2x}{x}$ yields the average cost in dollars for a company to produce $x$ copies of a comic book. which statement best fits the situation modeled by the function? the company earns 20 cents as profit from each copy sold. the company spends 20% of the issue price on materials to produce each copy. the company spends 20 cents on materials to produce each copy. the company earns 20% of the issue price as profit from each copy sold.

Explanation:

Step1: Analyze the function

The function is \( f(x)=\frac{80000 + 0.2x}{x}\). We can split this fraction: \( f(x)=\frac{80000}{x}+\frac{0.2x}{x}=\frac{80000}{x}+ 0.2\).

Step2: Interpret the terms

• The term \(\frac{80000}{x}\) represents a fixed cost per copy (since 80000 is a fixed cost, divided by the number of copies \(x\)).
• The term \(0.2\) is a constant cost per copy. Since \(0.2\) dollars is 20 cents, this means the company spends 20 cents on materials (or some variable cost) to produce each copy.

Now let's analyze each option:

• Option 1: Talks about profit, but the function is about average cost, not profit. Eliminate.
• Option 2: Talks about 20% of the issue price, but our term is a fixed 0.2 dollars (20 cents), not a percentage of a price. Eliminate.
• Option 3: Matches our interpretation of the \(0.2\) term (20 cents per copy for materials or variable cost).
• Option 4: Talks about profit percentage, but the function is about cost. Eliminate.

Answer:

The company spends 20 cents on materials to produce each copy. (Assuming this is the third option, if we consider the options as: 1. The company earns 20 cents as profit from each copy sold. 2. The company spends 20% of the issue price on materials to produce each copy. 3. The company spends 20 cents on materials to produce each copy. 4. The company earns 20% of the issue price as profit from each copy sold. Then the correct option is the third one, e.g., if the third option is labeled as C, then C. The company spends 20 cents on materials to produce each copy.)