* Suppose you are the economic advisor for a firm that is trying to decide whether to acquire ABC Oil Company, whose only asset is an oil field that has a net value X under its current management. The owners of ABC know the exact value of X but your company knows only that X is a random number that is uniformly distributed between 0 and 100. Because of your company's superior management, ABC's oil field would be worth X+30 in its hands.

(1) If your company bids P, describe the expected value of ABC's oil field to your company and the expected profit.

(2)What is the most your company can bid and not expect to take a loss?

(3)Assuming your company is the only bidder, what bid maximizes your company's expected profit?