The executive search being conducted for Western Bank by Headhunters Inc. may finally be bearing fruit. The position to be filled is a key oneVice President for Information Processing because this person will have responsibility for developing a state-of-the-art management information system that will link together Westerns many branch banks. However, Headhunters feels it has found just the right person, Matthew Fenton, who has an excellent record in a similar position for a mid-sized bank in New York.After a round of interviews, Westerns 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 Matthews salary, training, recruiting costs, and expenses). If he is not suc-cessful, the company will realize a net loss of $600,000.For an additional fee of $40,000, Headhunters will provide a detailed investigative process (including an extensive back-ground check, a battery of academic and psychological tests, etc.) that will further pinpoint Matthews potential for success. This process has been found to be 90 percent reliable, that is, a candidate who would successfully design the management infor-mation system will pass the test with probability 0.9, and a can-didate who would not successfully design the system will fail the test with probability 0.9.Westerns top management needs to decide whether to hire Matthew and whether to have Headhunters conduct the detailed investigative process before making this decision.

a) Use the likelihoods/conditional and prior probabilities to calculate all the posteriors/revised probabilities. Show your work/calculations.

b) Draw a decision tree for this problem that will help Westerns top management decide whether to hire Mathew and whether to have Headhunters conduct the detailed investigation process before making this decision. Solve the decision tree and determine the optimal decision strategy and its expected payoff. (Show your work/calculations). Verbally communicate the decision strategy.

c) Now suppose that the Headhunters fee for administering its detailed investigative process is negotiable. What is the maximum amount that Western Bank should pay? Show your work/calculations.