Problem 3. A firm produces 2 goods and has revenue R = P Q. + PQ2, where P, is the price of good i. Its costs of producing are C = 20; + Q.Q2 + 3Q2. The firm's goal is to maximize profits by choosing the optimal quantities (it takes the prices as given). 1 a 1. Solve for the critical values Qi and Q in terms of the prices. 2. Now suppose that P1 = 8 and P = 7. Find the quantities (Q and Q2) that maximize the firm's profits. Be sure to verify that your answer is a maximum rather than a minimum. What are the firm's profits at the optimal production levels