A publisher for a promising new novel figures fixed costs (overhead, advances, promotion, copy editing, typesetting, and so on) at $53,000 and variable costs (printing, paper, binding, shipping) at $2.20 for each book produced. If the book is sold to distributors for $12 each, how many must be produced and sold for the publisher to break even?

5,409 books

Explanation:

to calculate break even point in units we can use the following formula:

break even point in units = total fixed costs / contribution margin per unit

break even point in units = $53,000 / $9,80 = 5,408.16 ≈ 5,409 books

in $, that would equal = 5,409 books x $12 per book = $64,908

x = 5,408 Books

Explanation:

Cost equations

c(x) = 2.20x + 53,000

Revenue equation

r(x) = 12x

Break even is when Revenue = cost

12x = 2.20x + 53000

12x - 2.20x = 53000

9.8x = 53000

x = 53,000/9.8

x = 5,408 Books

Prove

Rev: 12(5,408) = $64,896.00

Cost: 2.20(5,408) + 53,000

=11,897.6+53,000= 64,897.6

Therefore 5,408 books must be produced and sold for the publisher to break even.