Question: Printing. A printer has a contract to run 20,000 posters for a state fair. He can use any number of plates from 1 to 8 to run the posters, so that each stamp of the press produces a number of posters equivalent to the number of plates that have been created. The cost of printing all the posters is given by

C(x) = 200 + 20x + \[\frac{180}{x}\], where x is the number of plates.

a) Combine the terms of this function over a common denominator to create a rational function.

b) Use numerical or graphical methods to find the number of plates that will make the cost $336.

c) How many plates should the printer create to produce the posters at the minimum cost?