Find the production cost function C(p).C(p)=$

Question

The marginal cost for printing a paperback book at a small publishing company is per page where  is the number of pages in the book.A  page book has a  production cost. Find the production cost function .0.02+

Answer 1

The marginal cost c(p)=0.02 is the derivative of C(p), which is the production cost. Be careful on this because the upper case C and lower case c are two different functions.

In that case, C(p) is the antiderivative of c(p). We have to integrate c(p).

C(p) = ∫0.02dp

C(p) = 0.02p + k, where k is constant

According to the problem, when p=840, C(p)=20.27. Plugin those values to solve for k.

20.27=0.02(840)+k

k=3.47

Therefore the production cost function will be:

C(p) = 0.02p + 3.47