1. Consider a firm with the production function (POINTS: 30) F(K,L) = K3'5L1/5 You will be solving the profit maximization for this firm with both the twostep and onestep methods and proving that the final answers are identical. (a) Setup and solve the long run cost minimization problem for the long run optimal amount of capital K*(q,w,r) and labor L*(q,w,r), and the long run minimized cost C*(q,w,r). (Points: 6/30) (b) Setup and solve the profit maximization problem over quantity using the cost function you solved for in the previous part. Solve for the profit maximizing quantity (1* (p,w, r}, cost C*(p,w,r). and 3*(p,w,r). (Points: 5/30) (c) Setup and solve the profit maximization problem over inputs. Solve for the profit maximizing amounts of capital K*(p,w,r}, labor L*(p,w,r), output F(K*,L*), cost C*(p,w,r). and 3*(p,w,r)- (Points: 6/30) (d) Prove that your answers in part B and part C give you the identical levels of profit maximizing output and profit. (Points: 9/30) (2) Does the firm exit in the long run? Prove how you know and Show all of your work. (Points: 3/30)