3. (6 points) Optimize the profit function for a firm: 22' = -7x2 - 4y2 + 8 xy + 8x + 4y + 1 by (a) finding the critical point at which the function may be optimized and (b) determining whether at this point the function is maximized or minimized. Must show your work. 4. (8 points) Find (a) the profit maximizing level of outputs, Q1 and Q2, and (b) the profit maximizing levels of prices, P1 and P2, for the monopolistic producer of two products 1 and 2 with the demand functions Q1 = 27 - 3P1 Q2 = 36 - 2P2 and the joint cost function C = 01 + 0102 + 02 + 120. [Make sure to check the second order conditions.]