Oilco must determine whether or not to drill for oil in the South China Sea. It cost $100,000, and if oil is found the value is estimated to be $600,000. At present, Oilco believes there is a 45% chance that the field contains oil. Before drilling, Oilco can hire (for $10,000) a geologist to obtain more information about the likelihood that the field will contain oil. There is a 50% chance that the geologist will issue a favorable report and a 50% chance of an unfavorable report. Given a favorable report, there is an 80% chance that the field contains oil. Given an unfavorable report, there is a 10% chance that the field contains oil.

a) What is the optimal choice under the maximin payoff criterion?

b) What is the optimal choice under the maximum likelihood criterion?

c) What is the optimal choice under Bayes' decision rule? What is the resulting expected payoff?

d) Conduct a sensitivity analysis of Bayes' decision rule. What is the cross over point? What does this point imply about the decision?

e) Find EVPI. Does this answer indicate that consideration should be given to using the research firm?

f) Assume that the research firm is used. Develop a probability tree diagram to find the posterior probabilities of the respective states of nature for each of the alternatives.

g) Find EVE. Does this answer indicate that consideration should be given to using the research firm?

h) Determine the optimal policy by drawing a decision tree.