4. Francisco and Priya (F&P) have developed an innovative new product. They have applied for a patent for their new innovation. They estimate that there is a 75% chance that the patent application will be approved by the U.S. Patent Office. F&P also presented their product to a large corporation ITNET, after having ITNET sign a confidentiality agreement. Yesterday, ITNET announced a new product suspiciously similar to F&P's innovative new product. Francisco's first impulse was to sue ITNET immediately. However, Priya feels that they should wait until they have received notification of whether their patent is approved. Priya reasoned that their case would be much stronger if they had a patent for their product. Suppose that F&P have an 88% chance of winning a lawsuit against ITNET if their patent application is approved, and that they still have a 60% chance of winning such a lawsuit while their patent application is under review. However, if their patent application is not approved, the chance of winning the lawsuit would drop to 40%. If F&P sue ITNET immediately (while the patent application is still under review), there is a 70% chance that ITNET would settle out of court for $400,000 and a 30% chance that ITNET would not settle out of court and the case would proceed to trial. If F&P win at a trial, the award would be $1.2 million and if they lose they get nothing. F&P estimate that the legal costs of a trial would be $200,000, regardless of whether they win or lose. If they wait until after the patent application has been reviewed to file the case, there is no chance that ITNET would settle out of court and the suit would go straight to trial. a) Use a decision tree to determine what F&P should do (e.g. when should they file their lawsuit). State the optimal decision strategy and its expected value. b) Draw a risk profile for the optimal decision strategy