2. A firm's technology is characterized by a Cobb-Douglas production function of the form y = f(K, L) = 3K1/2 + 5L1/2 a. The output price is p, and the input prices are r and w for K and L, respectively. Set up the problem for a profit-maximizing firm and solve for the factor demand functions for K and L. (20p) b. Find the firm's supply function. (10p) c. Find the firm's profit function. (10p) d. Assume now that p = 2, r = 1, and w = 1. Using the functions you have found in parts (a), (b) and (c), calculate the profit-maximizing levels of the factors (K* and L*), the profit- maximizing output level (y*) and the maximum profit of the firm (TT*). (10p)