Question 1. (30 points} Sam Ellis is the CEO of Forward Software, maker of Cinco, a spreadsheet program for personal computers (PCs). Cinco's main competitor is Focus A-E-C, which was the first spreadsheet introduced to the PC market. Currently Focus has filed suit against a 3rd spreadsheet maker, Discount Software, for copyright violation. Now Sam is worried that Focus may also sue Forward. After talking to his attomeys, Sam feels that if he makes a quiet overture to Focus to settle out of court, he would avoid potential negative publicity, and might cost the company less in the long run. He and his attorneys believe that Focus would accept the offer to settle, but the possible payments are uncertain. They think Focus could ask for $5, $0 or $15 million in damages, with probabilities .50, .30 and .20 respectively. Rather than settle out of court now, Sam could also wait to see the outcome of the suit against Discount Software. He believes that there is a 40% chance that Focus will win its suit against Discount. If they win, there is an 80% chance they will le suit against Forward. If Focus did file suit, Forward could again consider a settlement, or could go to court. If they settle after Focus wins its current suit, however, the settlement amounts would be higher: 35?, $10 and $12 million with respective probabilities .30, .40 and .30. In addition, Forward would have to pay its own attorneys $1 million to go through the settling process. If they decide to go to court, Sam and his attorneys estimate that Forward would have an 30% chance of losing, and if they lose there would be a 10% chance they would pay a judgment of $10 million, a 20% chance they would pay $12 million, and a T091\": chance they would pay $18 million. The attorneys also estimate that their fees for going to trial would be $1.5 million if they lose, and $1 million if they win. - Draw the influence diagram. - Draw the decision tree of the decision problem that Forward Software is facing. Be sure to clearly label the branches, include probabilities, outcomes, and results for expected prots. - Use the decision tree to determine the course of action that should be taken to maximize expected profit. What is the maximum expected profit? What is the best course of action? - Suppose Sarn has the opporhinity to hire a former judge who is an expert in copyright infringement cases. The judge makes predictions as to whether a defendant {like Forward) will win or lose their case. What would be the most Sam should ever consider paying to get extra information about his chances of winning the case