4. This problem will walk you through the producer's profit maximization problem with a fixed input. Once again, use the same prices and production function as before. Now the firm can sell its output at unit price p. (a) What is the firm's revenue if it sells y units of output? Recall that profit is revenue less production cost. If the firm produces y output while using inputs x1 and x2, what will be the firm's profit? (b) Suppose the firm wants to maximize its profit, choosing its output level and inputs. What is an expression that mathematically represents this problem. Just as in 1(b), think carefully about what is a choice variable, what the objective function is, and what the constraints are. (c) The two step procedure to maximize profit says that no matter how much output we produce, the firm wants to do so in the cheapest way possible. With this in mind, rewrite the maximization problem from 4(b) by substituting the cost function from 2(c). You should get the following expression; briefly explain it. max y py (10y^(3/2) + 40) (d) Take the derivative of the expression for profit from 4(c) with respect to y,