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Answered

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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 $66,755, and the variable costs will be $12.50 per book. With the other method, the one-time fixed costs will total $23,159, and the variable costs will be $23 per book. For how many books produced will the costs from the two methods be the same?

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Answer:

  4152 books

Step-by-step explanation:

As we will see when we write the equations, the number of books will be the difference in fixed costs divided by the difference in variable costs:

  (66755 -23159)/(23 -12.50) = 43596/10.5 = 4152

The costs of the two methods are the same for production of 4152 books.

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The costs for method 1 for production of b books are ...

  m1 = 66755 +12.50b

The costs for method 2 for production of b books are ...

  m2 = 23159 +23b

The two costs are equal when ...

  m2 = m1

  23159 +23b = 66755 +12.50b

  10.5b = 43596 . . . . . . . . . . . subtract 12.50b+23159 from both sides

  b = 43596/10.5 . . . . divide by the coefficient of b

  b = 4152 . . . . . . . . . book production to make the costs the same

For 4152 books produced, the costs from the two methods will be the same.

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