10 points) A firm is the sole producer of two goods labelled 1 and 2. The demand unctions are given by Q1 = 495 - P1 - P2 Q2 = 695 - P1 - 2P2 where Q: and P; denote the quantity demanded and price of good i, respectively. The total cost function is TC = Q3 + Q1Q2+ Q3 a) (4 points) Show that the profit function is given by IT = 29501 + 200Q2 + Q102 - 303 -203 b) (4 points) Find the values of Q1 and Q2 which maximise the profit and verify that the second order conditions for a maximum are satisfied. c) (2 points) Find the prices that the producer should charge to maximize profit