Story problem

Question

A publisher for a new novel figures fixed costs at $51,000, and variable costs at $2.10 for each book produced. If the book is sold to distributors for $14.00 each, how many must be produced and sold for the publisher to break even?

Answer 1

51,000+2.1*x=14*x

51,000=11.9*x

x=4285.7 -> round to the nearest whole number -> 4286 books need to be produced and sold in order to break even.

Answer 2

If b is the number of books produced, the 51000 + 2.1*b cost of production must equal 14*b the sale value of the books.

This ignores tax and shipping etc.

 

So 51000 + 2.1*b = 14*b, so b = 51000/(14-2.1) = 4285.71429. Rounding, we find b = 4286 books to break even.

Answer 3

x = # books sold

 

14x = 51,000 + 2.10x

11.90x = 51000

x = 4285.7 

 

Since you can't produce fractional books, they must produce and sell 4286 books.