Company SuperRich is considering the possibility of building an additional factory that would produce a new product. The company has two options. The first is 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 low demand is 0.6 and the chance of high demand is 0.4. Not constructing a new facility 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 before making the capacity decision. Construct a decision tree and conduct the analysis to determine the value of the oracle.

c. Suppose that Company SuperRich has an option of conducting a market research before making the capacity decision. We assume that the market research is not affecting the actual demand realization. If the research outcome is good, then the chance of high demand becomes 0.8 (and low demand is 0.2). Company SuperRich estimates that the probability of getting a good research outcome is 0.45. Construct a decision tree and conduct the analysis to determine the value of this market research.