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

The total cost function, \( C(x) \), can be expressed as the sum of the fixed costs and the variable costs associated with producing \( x \) bicycles.

1. The fixed cost is given as \( 80,000 \).
2. The variable cost per bicycle is \( 200 \), so for \( x \) bicycles, the variable cost will be \( 200x \).

Thus, the total cost function can be written as:

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

Now, to find \( C(110) \), we substitute \( x = 110 \) into the total cost function:

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

Calculating the variable cost:

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

Now, adding this to the fixed cost:

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

### Interpretation of \( C(110) \):
The value \( C(110) = 102,000 \) means that the total cost of producing 110 bicycles is $102,000. This includes both the fixed costs and the costs associated with the production of 110 bicycles.