Question

A small bicycle manufacturer has daily fixed costs of ​$1912 and each bicycle costs ​$73 to manufacture. Let x represent the number of bicycles manufactured and C(x) represents the cost of manufacturing.

Find the value of x if ​C(x)equals2715. Express this situation using function​ notation, and interpret it in the context of this problem.
xequals
  
enter your response here when ​C(x)equals2715. This means that the cost of manufacturing
  
enter your response here bicycles in a day is ​$
  
enter your response here.

Answer 1

To model the cost of manufacturing bicycles in function notation, we can express \(C(x)\), the total cost of manufacturing \(x\) bicycles, as follows:

\[
C(x) = \text{Fixed Costs} + \text{Variable Cost per Bicycle} \times \text{Number of Bicycles}
\]

Substituting the given values:

\[
C(x) = 1912 + 73x
\]

Now, we need to find the value of \(x\) when \(C(x) = 2715\):

\[
2715 = 1912 + 73x
\]

To solve for \(x\), we first subtract the fixed costs from both sides:

\[
2715 - 1912 = 73x
\]

Calculating the left side:

\[
803 = 73x
\]

Now, divide both sides by 73:

\[
x = \frac{803}{73} \approx 11
\]

Thus, \(x \approx 11\).

This means that when \(C(x) = 2715\), the cost of manufacturing 11 bicycles in a day is $2715.

Therefore, in complete interpretation:

- \(x\) equals **11** when \(C(x)\) equals 2715.
- This means that the cost of manufacturing **11** bicycles in a day is **$2715**.