A 15.4-8. Jose Morales manages a large outdoor fruit stand in one 15.4-11. Use the scenario given in Prob. 15.3.-1 1. of the less affluent neighborhoods of San Jose, California. To re- (a) Draw and properly label the decision tree. Include all the pay- plenish his supply, Jose buys boxes of fruit early each morning offs but not the probabilities. from a grower south of San Jose. About 90 percent of the boxes T (b) Find the probabilities for the branches emanating from the of fruit turn out to be of satisfactory quality, but the other 10 per- chance forks. cent are unsatisfactory. A satisfactory box contains 80 percent ex- (c) Apply the backward induction procedure, and identify the re- cellent fruit and will earn $200 profit for Jose. An unsatisfactory sulting optimal policy. box contains 30 percent excellent fruit and will produce a loss of $1,000. Before Jose decides to accept a box, he is given the op- 15.4-12. Use the scenario given in Prob. 15.3-12. portunity to sample one piece of fruit to test whether it is excel- (a) Draw and properly label the decision tree. Include all the pay- lent. Based on that sample, he then has the option of rejecting the offs but not the probabilities. box without paying for it. Jose wonders (I) whether he should con- T (b) Find the probabilities for the branches emanating from the tinue buying from this grower, (2) if so, whether it is worthwhile chance forks. sampling just one piece of fruit from a box, and (3) if so, whether (c) Apply the backward induction procedure, and identify the re- he should be accepting or rejecting the box based on the outcome sulting optimal policy. of this sampling. Use TreePlan (and the Excel template for posterior probabil- 15.4-13. Use the scenario given in Prob. 15.3-13. ities) to construct and solve the decision tree for this problem. (a) Draw and properly label the decision tree. Include all the pay- offs but not the probabilities. 15.4-9. Use the scenario given in Prob. 15.3-9. T (b) Find the probabilities for the branches emanating from the a) Draw and properly label the decision tree. Include all the pay- chance forks. offs but not the probabilities. c) Apply the backward induction procedure, and identify the re- T (b) Find the probabilities for the branches emanating from the sulting optimal policy. chance forks. (c) Apply the backward induction procedure, and identify the re- 15.4-14. Chelsea Bush is an emerging candidate for her party's sulting optimal policy. nomination for President of the United States. She now is consid 15.4-10.* The Morton Ward Company is considering the introduc- ering whether to run in the high-stakes Super Tuesday primaries. tion of a new product that is believed to have a 50-50 chance of be- If she enters the Super Tuesday (S.T.) primaries, she and her ad- ing successful. One option is to try out the product in a test market, visers believe that she will either do well (finish first or second) at a cost of $5 million, before making the introduction decision. Past or do poorly (finish third or worse) with probabilities 0.4 and 0.6. experience shows that ultimately successful products are approved respectively. Doing well on Super Tuesday will net the candidate's in the test market 80 percent of the time, whereas ultimately unsuc- campaign approximately $16 million in new contributions, whereas cessful products are approved in the test market only 25 percent of a poor showing will mean a loss of $10 million after numerous TV the time. If the product is successful, the net profit to the company ads are paid for. Alternatively, she may choose not to run at all on will be $40 million; if unsuccessful, the net loss will be $15 million. Super Tuesday and incur no costs. r (a) Discarding the option of trying out the product in a test mar- Chelsea's advisers realize that her chances of success on Su- ket, develop a decision analysis formulation of the problem per Tuesday may be affected by the outcome of the smaller New by identifying the alternative actions, states of nature, and Hampshire (N.H.) primary occurring 3 weeks before Super Tues- payoff table. Then apply Bayes' decision rule to determine day. Political analysts feel that the results of New Hampshire's pri- the optimal decision alternative. mary are correct two-thirds of the time in predicting the results of T (b) Find EVPI. the Super Tuesday primaries. Among Chelsea's advisers is a deci- A (c) Now including the option of trying out the product in a test sion analysis expert who uses this information to calculate the fol- market, use TreePlan (and the Excel template for posterior lowing probabilities: probabilities) to construct and solve the decision tree for this P[Chelsea does well in S.T. primaries, given she does problem. well in N.H. ] A (d) There is some uncertainty in the stated profit and loss fig- ures ($40 million and $15 million). Either could vary from P| Chelsea does well in S.T. primaries, given she does its base by as much as 25 percent in either direction. Use poorly in N.H. ] Sensit to generate a graph for each that plots the expected payoff over this range of variability. P[Chelsea does well in N.H. primary ] 15
