Question: A machine shop owner is attempting to decide whether or not to purchase a new drill press, a lathe, or a grinder. The return from each will be determined by whether the company succeeds in getting a government military contract. The profit or loss from each purchase and the probabilities associated with each contract outcome are shown in the following payoff table:

Purchase Contract .40 No Contract .60

Drill press $40,000 $ -8,000

Lathe 20,000 4,000

Grinder 12,000 10,000

Compute the expected value for each purchase and select the best one

The machine shop owner is considering hiring a military consultant. By talking to other machine shop owners and obtaining past data, the owner has estimated the military consultant was correctly issued a favorable report where a contract was later award 70% of the time, P(f | c) = 0.70. Also, the military consultant correctly issued an unfavorable report where no contract was awarded 80% of the time, P(u | n) = 0.80. Using decision tree analysis, compute the maximum fee the owner should pay the consultant for his services.