I need help constructing decision tree plans please.

Problems 26,27,31

3-26 A group of medical professionals is considering con- structing a private clinic. If patient demand for the clinic is high, the physicians could realize a net profit of $100,000. If the demand is low, they could lose $40,000. Of course, they don't have to proceed at all, in which case there is no cost. In the absence of any market data, the best the physicians can guess is that there is a 50-50 chance that demand will be good. (a) Construct a decision tree to help analyze this problem. What should the medical professionals do? (b) The physicians have been approached by a mar- ket research firm that offers to perform a study of the market at a fee of $5,000. The market researchers claim that their experience enables them to use Bayes' theorem to make the follow- ing statements of probability: probability of high demand given a positive study result = 0.82 probability of low demand given a positive study result = 0.18 probability of high demand given a negative study result 0.11 probability of low demand given a negative study result - 0.89 probability of a positive study result = 0.35 probability of a negative study result - 0.45 Expand the decision tree in part (a) to reflect the op- tions now open with the market study. What should the medical professionals do now? (c) What is the maximum amount the physicians would be willing to pay for the market study? 2 delete mm 3-27 In Problem 3-26, you helped a group of medical profes- sionals analyze a decision, using EMV as the decision criterion. This group has also assessed its utility for money: U(-$45,000) = 0, U(-$40,000) = 0.1, U(-$5,000) = 0.7, U($0) = 0.9, U($95,000) = 0.99, and U($100,000) = 1. (a) Are the medical professionals risk sekers or risk avoiders? Justify your answer. (b) Use expected utility as the decision criterion and determine the best decision for the medical pro- fessionals (including the option to use the mar- ket research firm). 3-28 Jerry Young is thinking about opening a bicycle shop in his hometown. Jerry loves to take his own bike on 50-mile trips with his friends, but he believes that any small business should be started only if there is a good chance of making a profit. Jerry can open a small shop, a large shop, or no shop at all. Because there will be a five-year lease on the building that Jerry is thinking about using, he wants to make sure that he makes the correct decision. Jerry has done some analysis about the profit- ability of the bicycle shop. In Jerry builds the large bicycle shop, he will earn $60,000 if the market is good, but he will lose $40,000 if the market is bad. The small shop will return a $30,000 profit in a good market and a $10,000 loss in a bad market. At the present time, he believes that there is a 59% chance that the market will be good Jerry also has the option of hiring his old mar keting professor for 55.000 to conduct a marketing research study. If the study is conducted, the results could be either lavorable or unfavorable. It is esti mated that there is a probability that the survey is 0. valy. 0.6 p of the the or cents. it will than su (a) De: deci (b) For an or manu supp! 3-30 After ob received prising stu vice in his in a new hd of $700 if $200 if it is As per the c ties of heavy are 0.4.0.3.3 Rather th get his fathe smaller jobs. profit of $350 for a moderato light snowfall choosing neithe The local is Ajay's good run sophisticated C u mb.umassonline.netbbcswebdav/pid-3484056-dr-content-rid-28260508 1/courses/82930-8044/Problems Cn. PERCENTAGE PRORABILITY PROFILITY 3-31 Oscar Weng is planning to raised to pay for a DEFECTIVE FOR SUPPLIERA FOR SUPPLIER scouting trip by using a concession stand during tomorrow's high school accer game. Oscar needs to decide whether to rent a large insulated thermos from the local rental store and sell cocoa the game or to rent a large refrigerated container and sell lemonade. DISCUSSION QUESTIONS AND PROBLEMS 67 Unfortunately Oscar does not have the resources to rent buchem Sales depend whether it is of my during the game. If the weather is sunny Oscar will make a profit of Sh from le d e bu only $30 from cocoa 1. however, it is niny, Oscar will make a proof of hotely break even if he brings lemonade. Based on the local w er's prediction car thinks there is will setits price high, medium, and low is 0.15 025, and respectively No Flight has no competition for its new golf halls, its expected payed for setting the price high medium, and low is S00,000, SSD , and SOLO respectively, excluding marketing costs Do you end marketing the new golfhall so, what is your pricing recommendation Your tar tennispartner beside friendly waper with you. The of you will play out one points which you care. The lose the win ter sof your first serveis i play you get a securednisolo Y e ar yo u r hand 3. Me he dichter more way thus the newspaper Tools offers to the wholl O there is cho had chance of the that . They will the 75th Yey