Southern Gas Company $($SGC$)$ is preparing to bid for oil and gas leasing rights in a newly opened drilling area in the Gulf of Mexico. SGC is trying to decide whether to place a high bid of $$16$ million or a low bid of $$7$ million. SGC expects to be bidding against its major competitor, Northern Gas Company $($NGC$),$ and predicts NGC to place a bid of $$10$ million with a probability of $0\mathrm{.}4$ or a bid of $$6$ million with a probability of $0\mathrm{.}6.$ Geological data collected at the drilling site indicates a $0\mathrm{.}15$ probability of the reserves at the site being large, a $0\mathrm{.}35$ probability of being average, and a $0\mathrm{.}50$ probability of being unusable. A large or average reserve would most likely represent a net asset value of $$120$ million or $$28$ million, respectively, after all drilling and extraction costs are paid. The company that wins the bid will drill an exploration well at the site for a cost of $$5$ million.