3. Consider a Cournot duopoly model where the market price is given by the inverse demand function: p = 30 - 3 . q1 - 92. And suppose each firm produces at a cost of 25 per unit of production (i.e, total costs are given by 25 . qi for i = 1, 2). (a) Find the payoff functions u1 (91, 92) and u2 (91, 92). (b) Suppose player 1 believes that player 2 is equally likely to produce q2 = 10, 92 = 15, q2 = 18 and q2 = 22 units, and these are the only production values player 1 believes player 2 can choose. Let 02 denote these beliefs for player 1. Compute u1 (91, 02) for these beliefs 02. (c) Suppose player 2 believes that player 1 will produce q1 = 13 with probability 1/3, q1 = 10 with probability 1/4, and q1 = 16 with probability 5/12, and these are the only production values player 2 believes player 1 can choose. Let 61 denote these beliefs for player 2. Compute u2 (01, q2) for these beliefs 01