Problem: Company SuperRich is considering the possibility of capacity expansion. The company has three options. The first is to build a small facility that it could build at a cost of $5 million. If demand for new products is low, the company expects to receive $7 million in revenue with the small facility; if demand is high, it expects $12 million in revenues using the small facility. The second option is to build a large factory at a cost of $10 million. If demand is low, the company would expect $9 million in revenues with the large plant; if demand is high, the revenue is expected to be $20 million. In either case, the chance of high demand is 0.4 and low demand is 0.6. The third option is not to construct any new facility, which will lead to $5 million revenue regardless of the demand condition.
a. Construct a decision tree and conduct the analysis to help company SuperRich to make the best decision.
b. Suppose that there is an oracle telling Company SuperRich whether the demand is high or low (according to the true probability, which is 0.4 for high demand and 0.6 for low demand) before making the decision. Construct a decision tree and conduct the analysis to determine the value of the oracle.