Question

A small publishing company is planning to pubilsh a new book. The production coast will include one-time fixed cost (such as editing) and variable costs ( such as printing) There are two production methods it could use. with one method, the one-time fixed costs will total $22,256, and the variable costs will be $25 per book. with other method, the one -time fixed costs will total $80,768, and the variable costs will be $11.75 per book. For how many books produced will the costs from the two methods be the same.

Answer 1

In the question, we are given the following information about the production cost of the two methods.

For method 1, the one-time fixed costs will total $22,256, and the variable costs will be $25 per book.

For method 2, the one-time fixed costs will total $80,768, and the variable costs will be $11.75 per book.

This is a case of partial variation and we can derive two equations for the different production methods using the formula below.

`\begin{gathered} \text{Production cost=fixed cost +variable cost} \\ \end{gathered}`

Let each book represents b

Thus;

`\begin{gathered} \text{Method 1;} \\ 25b+22256=\text{ Production cost} \\ \text{Method 2;} \\ 11.75b+80768=\text{Production cost} \end{gathered}`

To find the number of books produced that would make the costs from the two methods be the same, we would equate the equations above;

`\begin{gathered} 25b+22256=11.75b+80768 \\ 25b-11.75b=80768-22256 \\ 13.25b=58512 \\ \text{Divide both sides by 13.25} \\ (13.25b)/(13.25)=(58512)/(13.25) \\ \therefore b=4416 \end{gathered}`

Therefore, the number of books produced that would make the costs from the two methods be the same is;

Answer: 4416