Question

A company that manufactures bicycles has a fixed cost of $80,000. It costs $200 to produce each bicycle. The
total cost for the company is the sum of its fixed cost and variable costs. Write the total cost, C, as a function of
the number of bicycles produced, x. Then, find and interpret C(110).
The total cost function is C(x) =

Answer 1

To write the total cost \( C \) as a function of the number of bicycles produced \( x \), we start by noting that the total cost consists of fixed costs and variable costs.

1. **Fixed Costs**: The fixed cost is a constant amount that does not change with the number of bicycles produced. In this case, the fixed cost is \$80,000.

2. **Variable Costs**: The variable cost is the cost per unit produced multiplied by the number of units produced. Here, it costs \$200 to produce each bicycle. Therefore, the variable cost for \( x \) bicycles is \( 200x \).

The total cost \( C(x) \) can be expressed as the sum of the fixed cost and the variable cost:

\[
C(x) = \text{Fixed Costs} + \text{Variable Costs} = 80,000 + 200x
\]

So the total cost function is:

\[
C(x) = 80,000 + 200x
\]

Next, we need to find \( C(110) \):

\[
C(110) = 80,000 + 200(110)
\]

Calculating \( 200(110) \):

\[
200 \times 110 = 22,000
\]

Now substitute back into the equation:

\[
C(110) = 80,000 + 22,000 = 102,000
\]

### Interpretation of \( C(110) \)

The value \( C(110) = 102,000 \) indicates that the total cost of producing 110 bicycles is \$102,000. This includes both the fixed costs and the variable costs associated with making those bicycles.