Assume that a monopoly's production function is Cobb-Douglas, Q = L^1/2 * K^1/2, where L is labor and K is capital. The demand function is P = 100 - Q. The wage rate, wL, is $1 per hour, and the rental rate of capital, wK, is $4 per hour.

(a) Derive the long-run total cost curve equation as a function of Q.

(b) What are the monopoly's profit maximizing price and quantity?

(c) Find the optimal input combination that produces the profit-maximizing quantity.