Question

Suppose you write a book. The printer charges $4 per book to print it, and you spend $3500 on advertising. You sell the book for $15 a copy. How many copies must you sell so that your income from sales is greater than your total cost?

Answer 1

I must sell more than 318 copies so my revenue is greater than my costs

Explanation:

The cost function (C(x)) is divided in two: fixed costs and variable costs. In this case, we have both, the fixed costs are $3,500 that I will spent on advertising and the variable cost is the print cost that depends on the number of books i want to print. The cost function is:

C(x)= $3,500+$4x

The revenue function depends on the number of books I sell:

R(x)= $15x

If i want to know how many books I should sell to have a greater revenue than cost i must solve this inequality:

Revenue (R(x))>Cost (C(x))

$15x>$3,500+$4x

$15x-$4x>$3,500

$11x>$3,500

x>$3,500/$11

x> 318,18

I must sell more than 318 copies so my revenue is greater than my costs