3. [8 points] Consider a variation of the industry we studied in Question 1. Again we have two profit-maximizing firms, A and B, that engage in price competition with differentiated products. Again each firm has to decide on a price for its own product; and if firm A charges price PA and firm B charges price PB. the demand for firm A's product is QA = 10 - PA+ PB and the demand for firm B's product is QB = 16 + PA - PB. Again, both firms have a constant marginal cost of $2 per unit and no fixed cost. But in this industry firm A first sets its price PA (and commits to it no matter what firm B does subsequently). Then firm B decides on PB after it learns the price of firm A. We can thus model this situation as a game in extensive form with perfect information. Solve this game by Backward Induction, and find the prices (PA, PB) charged by the two firms in the Backward Induction solution. Show your reasoning