1. (Decision Tree Problem) The president of Solar Phasic Industries, Jayne Cash, is interested in buying the Hi Voltage Transformer Company. She sees the possibility of large prots occuring to Hi Voltage if business is good. If she purchases the company now, large returns can be made in 2 years, when it would be sold. Hi Voltage's stock is currently held by two families, the Edisons and Franklins. The Edisons and Franklins have agreed to sell all their stock now for $1 Million, or half now for $600000 and the rest in 1 year based on the prot picture that time. Jayne Cash sees the following alternatives available to her. 0 One is to buy all the stock now and sell at the end of 2 years. On the other hand, if she buys only half now, she can purchase the rest in 1 year and sell at the end of 2 years. 0 Or she could hold her initial purchase initial purchase and not buy the second half, then sell at the end of the second year. A third alternative is not to purchase any stock and instead buy 2-year treasury bills. Jayne's payoffs are inuenced by business conditions. If business is good the company's rst year, the price of the second 50% of the stock will be $800000. If business is bad, the remainder of the stock will sell for $300000. However, if business is good the rst year, it may be bad during the second, and vice versa. All these events inuence what payoffs could be when Jayne plans to sell her shares of Hi Voltage. To resolve the chances of these states of nature facing Jayne Cash, G.N. Potter, Solar's chief economist, was called in to develop estimates of future events. Potter gathered data and projected future events. He stated that in the rst year, there would be a 60% chance of good business and 40% of bad. In the second year, if business were good in rst, there would be a 70% chance it would be good in the second and 30% chance that it would be bad. If the rst year were bad, there would be a 40% chance of good times and 60% of bad in the second year. Colleen Smart, Solar's chief system analyst, was also called on to help. She computed the net present value (NPV) of all possible alternatives available, based on the expected payoffs for each possible outcome. These are presented in Table 1. Business Condition Alternative Year 1 Year 2 NPV (Payoff) ($1000) Buy 100% Good Good 800 (Single Purchase) Good Bad -500 Bad Good 600 Bad Bad -700 Buy 50% Good Good 300 Good Bad 0 Bad Good 100 Bad Bad -100 Buy 100% Good Good 600 (Double Good Bad -600 Purchase) Bad Good 500 Bad Bad -400 Buy treasury bills 50 2. Table 1. Possible payoffs for buying Hi Voltage stock Jayne Cash can reap up to 3800.000 or lose 8700.000, depending upon what decision she makes and the events that occur in the future. Jayne sat at her desk reviewing the information from Potter and Smart. She will have to make a decision in the next few days or lose the opportunity to buy into the company. The Edison and Franklin Families have received other inquiries about selling. a) Develop a decision tree for Jayne Cash (you can use QM for Windows Decision Tree module or you can depict manually). b) What do you recommend? What is the best solution for Jayne Cash? Explain. (Employee Scheduling LP Application) UCSF Medical Center in LA. has foreseen a fairly well raise its revenue at the lowest possible cost for nurses. Regarding the medical center's patient density at different times of the year, Mr. Smith, the operation manager has anticipated the service hours required from the center's nurses for each 3-month period in a year, has been projected in the following table. Period (3-month) Period 1 Period 2 Period 3 Period 4 Service hours required 90,000 96,000 [20,000 135,000 Mr. Smith envisions that in order to obtain an excellence in service performance, experienced senior nurses should assist new junior nurses by giving training on the work that needs to be done in the center and preparing them for their duty by conveying their work- related experience within a period of 3 months. In the hospital, a senior nurse would work 300 hours for each period. However, this experience transfer process results in a 120 hours reduction in working hours of senior nurses for each period. In this process, junior nurses have a monthly salary of $6,000 while a senior nurse is paid $7,000 for each month by the end of this year. Aer a 3-month training period, junior nurses' monthly salaries increase to $7,000. On the other hand, despite gaining experience and increased salaries, nurses they can leave the job due to busy worldng hours and training program with a 10% churn rate. There are 300 senior nurses at the beginning of the rst period. Mr. Smith wants to develop a schedule for hiring nurses in order to achieve an effective health service for patients of the center. Formulate and solve the LP problem indicating how many junior and senior nurses should be hired per period with the total cost for the nurse schedule of UCSF Medical Center by using QM for Windows Linear Programming Module. Report your ndings with suitable interpretations