1. Formulate the following decision problem using a decision tree. Danny, who has been injured by Manny in an automobile accident, has applied to Manny's insurance company for compensation. The company has responded with an offer of $10,000, Danny is considering hiring a lawyer to demand $50,000. If Danny hires a lawyer to demand $50,000, Manny's insurance company will respond by either offering $10,000 again or offering $25,000. If they offer $25,000, Danny plans to take it. If they offer $10,000, Danny will decide whether or not to sue. If he decides not to sue, he will get $10,000. If he decides to sue, he will win or lose. If he wins, he can expect $50,000. If he loses, he will get nothing. (To simplify this problem, ignore Danny's legal fees, and the emotional, temporal, and other costs of not set- tling for $10,000.)