A smoothie store has fixed monthly costs of $1200 for rent, utilities and employ salaries. They charge $4 each smoothie and it costs them $1 to make each smoothie. If x smoothies are produced and sold per month, find the following:

(a) A linear cost function C(x)

(b) A linear revenue function R(x)

(c) A linear profit function P(x)

(d) Determine the profit when 200 smoothies are produced and sold.

(e) How many smoothies will the store have to produce and sell in order to begin making a profit?

(i.e. What is the break even point?)