When hotdogs are sold for $5, approximately 700 are sold. When the price is raised to $6, the quantity demanded drops to 500. The initial cost is $200 and the cost per hotdog is $1. Assume that the demand function is linear. How many hotdogs at what price will yield maximum profit? Let x be the number of hotdogs.

a) Find the demand function p(x) as a function of x.

b) Find the revenue function R as a function of x. c) Find the cost function C as a function of x. d) Find the profit function P as a function of x e) How many hotdogs at what price will yield a maximum profit?