The executive search being conducted for Western Bank by Headhunters Inc. may finally be bearing fruit. The position to be filled is a key one—Vice President for Information Processing—because this person will have responsibility for developing a state-of-the-art management information system that will link together Western’s many branch banks. However, Headhunters feels they have found just the right person, Matthew Fenton, who has an excellent record in a similar position for a midsized bank in New York.

After a round of interviews, Western’s president believes that Matthew has a probability of 0.7 of designing the management information system successfully. If Matthew is successful, the company will realize a profit of $2 million (net of Matthew’s salary, training, recruiting costs, and expenses). If he is not successful, the company will realize a net loss of $400,000.

For an additional fee of $20,000, Headhunters will provide a detailed investigative process (including an extensive background check, a battery of academic and psychological tests, etc.) that will further pinpoint Matthew’s potential for success. This process has been found to be 90 percent reliable; i.e., a candidate who would successfully design the management information system will pass the test with probability 0.9, and a candidate who would not successfully design 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 investigative process before making this decision.

(a) Construct the decision tree for this problem.

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(b) Find the probabilities for the branches emanating from the chance nodes.

(c) Analyze the decision tree to identify the optimal policy.

(d) Now suppose that the Headhunters’ fee for administering its detailed investigative process is negotiable. What is the maximum amount that Western Bank should pay?