... fruit. The positionto be filled is a key one—Vice President for Information Processing—
because this person will have responsibility for developinga state-of-the-art management information system that will linktogether Western’s many branch banks. However, Headhuntersfeels they have found just the right person, Matthew Fenton, who has an excellent record in a similar position for a midsized bankin New York.
After a round of interviews, Western’s president believes that
Matthew has a probability of 0.7 of designing the management informationsystem successfully If Matthew is successful, the companywill realize a profit of $2 million (net of Matthew’s salary,training, recruiting costs, and expenses). If he is not successful, thecompany will realize a net loss of $400,000.
For an additional fee of $20,000, Headhunters will provide adetailed investigative process (including an extensive backgroundcheck, a battery of academic and psychological tests, etc.) that willfurther pinpoint Matthew’s potential for success. This process hasbeen found to be 90 percent reliable; i.e., a candidate who wouldsuccessfully design the management information system will passthe test with probability 0.9, and a candidate who would not successfullydesign the system will fail the test with probability 0.9.
Western’s top management needs to decide whether to hire
Matthew and whether to have Headhunters conduct the detailed investigativeprocess before making this decision.
(a) Construct the decision tree for this problem.
(b) Find the probabilities for the branches emanating from thechance nodes.
(c) Analyze the decision tree to identify the optimal policy.
(d) Now suppose that the Headhunters’ fee for administering itsdetailed investigative process is negotiable. What is the maximumamount that Western Bank should pay?