The chief executive officer of a firm in a highly competitive industry believes that one of her key employees is providing confidential information to the competition. She is 90% certain that this informer is the vice president of finance, whose contacts have been extremely valuable in obtaining financing for the company. If she decided to fire this vice president and he is the informer, she estimates that the company will gain $500,000. If she decides to fire the vice president but he is not the informer, the company will lose his expertise and still have an informer within the staff; the CEO estimates that this outcome would cost her company about $2.5 million. If she decides not to fire this vice president, she estimates that the firm will lose $1.5 million regardless of whether he actually is the informer (because in either case the informer is still with the company).

Before deciding whether to fire the vice president for finance, the CEO could order lie detector tests. to avoid possible lawsuits, the lie detector tests would have to be administered to all company employees, at a total cost of $150,000. Another problem she must consider is that the available lie detector tests are not perfectly reliable. In particular, if a person is lying, the test will reveal that the person is lying 95% of the time. Furthermore, if a person is not lying the test will indicate that the person is not lying 85% of the time.

a. To minimize the expected total cost of managing this difficult situation, what strategy should the CEO adopt?

b. Should the CEO order the lie detector tests for all of her employees? explain why or why not?

c. Determine the maximum amount of money that the CEO should be willing to pay to administer the lie detector tests.

d. How sensitive are the results to the accuracy of the lie detector test? are there any reasonable values of the error probabilities that change the optional strategy?

38. Carlisle Tire and Rubber, Inc., is considering expanding production to meet potential increases in the demand for one of its tires products. Carlisle's alternatives are to construct a new plant, expand the existing plant, or do nothing in the short run. The market for this particular tire product may expand, remain stable, or contract. Carlisle's marketing department estimates the probabilities of these market outcomes as 0.25, 0.35, and 0.40, respectively. The file P.09_38.xlsx contains Carlisle's estimated payoff (in dollars) table.

a. Use PrecisionTree to identify the strategy that maximizes this tire manufacturers expected profit.

b. Perform a sensitivity analysis on the optimal decision, letting each of the monetary inputs vary one at a time plus or minus 10% from its base value, and summarize your findings. In response to which monetary inputs is the expected profit value most sensitive?

39. a local energy provider offers a landowner $180,000 for the exploration rights to natural gas on a certain site and the option for future development. This option, if exercised, is worth an additional $1,800,0000 to the landowner, but this will occur only if natural gas discovered during the exploration phase. The landowner, believing that the energy company's interest in the site is a good indication that gas is present, is tempted to develop the field herself. To do so, she must contract with local experts in natural gas exploration and development. The initial cost for such a contract is $300,000, which is lost forever if no gas is found on the site. If gas is discovered, however, the landowner expects to earn a net profit of $6,000,000. The landowner estimates the probability of finding gas on this site to be 60%.

a. Create a payoff table that specifies the landowner's payoff (in dollars) associated with each possible decision and each outcome with respect to finding natural gas on the site.

b. Use PrecisionTree to identify the strategy that maximizes the landowner's expected net earnings from this opportunity?

c. Perform a sensitivity analysis on the optimal decision, letting each of the inputs vary one at a time plus or minus 25% from its base value and summarize your findings. In response to which model inputs is the expected profit value most sensitive?