Legal decision making is both costly and risky. Therefore, the tools of decision analysis can be readily applied to provide advice. The law firm of Lusht, Thomas \& Whiteman (LTW) is representing a company in an important civil case. They are the plaintiff and if the case is successful the firm and LTW stand to make a sizable settlement. However, LTW is faced by a difficult decision. The defendant has offered a settlement of $3 million to avoid going to court. If they proceed to court, LTW believes that one of three outcomes will occur. Either their client will be successful (a guilty verdict) in which case they will earn an estimated settlement of $8 million, their client will be unsuccessful (an innocent verdict) in which case they will earn nothing, or the jury will fail to reach a verdict in which case LTW expects that they will be forced to accept a lower settlement offer of $1 million. The cost of going to court is estimated at $500,000. Given LTW's extensive experience with cases like this, they estimate the probabilities of the various court outcomes as follows: Assuming LTW is interested in maximizing the long term payoffs of their client, construct a decision tree to answer the following question. 1. Should LTW accept the current settlement offer? Worried about the highly uncertain nature of the outcome, LTW has decided to gather more information before deciding whether to accept the settlement. In order to do this, they will conduct a jury study. A jury study is essentially a mock trial that allows the firm to judge the likely success of the eventual court case. The outcome of the jury study will be either a positive report or a negative report. Since the jury study is not exactly the same as a trial, the information it provides is not perfect. However, in past jury studies, whenever the eventual court case has resulted in a guilty verdict, the jury study had given a positive report 70% of the time and a negative report 30% of the time. Whenever the eventual court case was innocent, the jury study had given a positive report only 20% of the time and a negative report 80% of the time. Finally, whenever the court case resulted in no verdict, the jury study gave a positive report 50% of the time and negative report 50% of the time. Construct a decision tree to answer the following questions. 2. What is the optimal strategy given the jury study? 3 . What is the expected value of the optimal strategy? While the firm can obviously see the value of such a study, they are also concerned about whether it is worth it. Therefore they have asked LTW about how much such a study costs. 4. What is the maximum that they should be willing to pay for the jury study