(Class 4) [30 points] An online retailer specializing in custom dog toys is considering launching brick-and-mortar stores in Upstate South Carolina. They have an opportunity to open a spot on Woodruff Road in Greenville next month at an upfront cost of $50,000. They believe this location has a 60% chance of success and a 40% chance of failure. If the location is successful, then it will bring the company a total of $350,000 in net profits over its lifetime. If the location is unsuccessful, then it will lose the company an additional $100,000. Complicating the Woodruff Road location decision is the fact that the company has identified an additional location in downtown Clemson. They do not need to decide on opening this additional location now; they need to decide in about 11 months whether to open it 12 months from now. The Clemson location has an upfront cost of $30,000. Without any additional information, the company believes it has a 70% of success and a 30% chance of failure. If it is successful, it will bring the company a total of $300,000 in net profits over its lifetime but if it is unsuccessful, then it will lose the company an additional $150,000. There is enough time for the company to launch the Woodruff Road location and observe its success before needing to decide on the Clemson location. If they open the Woodruff Road location and it is unsuccessful, then the company does not have the additional capital to open the Clemson location. However, if the company opens the Woodruff Road location and it is successful, then there will be enough capital and the Clemson location has a 85% chance of being successful. In other words, P (Clemson location is successful | Woodruff Road is successful )=.85. Hint: Note that this is a probability that will appear in your decision tree - so there is not a need to apply Bayes Theorem here. (a) (15 points) Provide the decision tree for this company in terms of opening the two locations. Provide all probabilities of the branches leaving the chance nodes, as well as the terminal payoffs of any terminal branches. (b) (15 points) Solve the decision tree in order to determine the optimal sequence of decisions. Be sure to label the expected payoffs for all chance nodes, the expected payoffs for all event nodes, and the selected decisions for all event (decision) nodes