QUESTION 3 A. ArmaCo must determine whether or not to drill for oil at the Northern part of Jubail. It costs $100,000 to drill, and if oil is found, the value is estimated to be $600,000. At present, ArmaCo believes there is a 45% chance that the field contains oil with the profit payoffs give in the table below. State of Nature Alternatives Oil Dry Drill -100 No Drill 0 500 0 a. [0.5 Mark] Show the decision tree for the situation. b. Which alternative should the Armaco choose using: i. [1 Mark] the optimistic approach ii. [1 Mark] the conservative approach iii. [1 Mark] the minimax regret approach. c. [1 Mark] Determine which alternative should be chosen based on expected value. d. [1 Mark] Determine the expected value with perfect information. e. [1 Mark] Determine the expected value of the perfect information. B. Before drilling, ArmaCo 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. f. [1 Mark] Show the decision tree for the situation. g. [1 Mark] Determine ArmaCo's optimal course of action. h. [0.5 Mark] How much is the expected profit? i. [1 Mark] Determine the Expected Value of Sample Information