Find Cost Fucntion

Question

The marginal cost for printing a paperback book at a small publishing company is
c(p) = $0.013 per page where p is the number of pages in the book
A 620-page book has a $20.68 production cost. Find the production cost function C(p).

 

C(p) = $?

Answer 1

620 page book has total cost = 20.68 = TC = VC + FC = Variable Cost + Fixed Cost

= 20.68/620 per page = about .033355 per page = about 3 cents per page

MC = .013 per page = Marginal cost per page

C(p) = MC when p=1

C(p) = .013p for p = any number of pages

C(620) = .013(620) = $8.06

MC is the derivative of Total Cost with respect to p = about (.033355p)' = .033355

TC= integral of MC = .033355p