Need a function for sale-able books and its domain.

Question

The printing and binding cost for a book is $10. The editorial cost is $200,000. the first 2500 books are samples and are given free to professors. Let x be the number of books produced. Write a function describing the average cost of saleable books. State its domain.

Answer 1

Kate, I hope I'm not too late to help! Let's let C = the total cost of sellable books.

 

If x = the number of books produced altogether, then the sellable books are what is more than 2500, right?  If we produce 3500 books, then 1000 are for sale, or the books produced minus the samples.

 

If each of those 1000 books cost $10 to make, then they cost 10 x 1000 = $10,000.  Since we got that 1000 by subtracting 3500 - 2500, the total cost is then 10(x - 2500).

 

We also have the editorial cost, which has to be added, so we have C = 10(x - 2500) + 200,000

 

The domain is the values that x can be.  Since we are talking about sellable books, then there has to be more than 2500 books produced altogether, so x > 2500.

 

Hope this helps!