(1) The price p (in dollars) and the demand x for a particular steam iron are related by the equation p = 200 1/30x

and the cost is given by C(x) = 72000 + 60x.

Answer all of the following questions related to the given situation.

(a) Find the revenue function. Find the marginal revenue function.

(b) Find the profit function. Find the marginal profit function.

(c) Solving by hand, determine how many steam irons the company must sell to break even.

(d) Use the marginal profit function to create a sign chart and determine the number of steam irons that will create a maximum profit. What is the maximum profit?

(e) Graph the revenue and cost functions and shade the area that represents a positive profit. Mark the maximum profit point on the same graph.