Question

A company manufactures high-end racing bicycles. The total cost to manufacture 28 bikes is $28320. The daily fixed costsare $2000. Fixed costs refers to expenses that must be paid even when producing zero bikes, such as rent, utilities, etc.Assume that total cost, C, is linearly related to the number of bicycles, x, that the company manufactures.A) The cost function is:___B) The total cost to manufacture 24 bikes is $_____C) The cost to produce each additional bike is $_____

Answer 1

Given:

The total cost to manufacture 28 bikes is $28320.

The daily fixed costs are $2000

Assume that total cost, C, is linearly related to the number of bicycles, x, that the company manufactures

The relation between C and x will be as follows:

`C=mx+2000`

Substitute with x = 28, and C = 28320, to find the value of m

`28320=m\cdot28+2000`

Solve the equation to find (m)

`\begin{gathered} 28320-2000=28m \\ 26320=28m \\ m=(26320)/(28)=940 \end{gathered}`

So, the answer will be as follows:

A) The cost function is: C = 940x + 2000

B) The total cost to manufacture 24 bikes is $24,560

C) The cost to produce each additional bike is $940