Problem Page A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable

Question

Problem Page
A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (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
$65,054
, and the variable costs will be
$8.25
per book. With the other method, the one-time fixed costs will total
$12,539
, and the variable costs will be
$19.50
per book. For how many books produced will the costs from the two methods be the same?

Answer 1

This is just a slight various of a break-even problem.  Just set the 2 equations equal to each other.

 

First equation:        TC=8.25x+65054

Second equation:  TC=19.50x+12539

 

19.50x+12539=8.25x+65054

 

Subtract 8.25x from both sides; also subtract 12539 from both sides; which gets you:

 

11.25x=52515

 

Divide both sides by 11.25, to give you the break-even quantity (where both are the same quantity):

 

x=4,668 units