Monica is looking into the possibility of starting a small company to produce small sailboats for the recreational market. Unlike other mass-produced sailboats, however, these boats will be made specifically for children between 10 and 15. The boats will be of the highest quality and extremely stable, and the sail size will be reduced to prevent problems with capsizing. Her basic decisions are to build a large manufacturing facility, a small manufacturing facility, or no facility at all. With a favorable market, Monica can expect to make $90000 from the large facility or $60000 form the small facility. If the market is unfavorable, she will likely lose $30000 with a large facility and $20000 with a small facility. She estimates that the probability of a favorable market is 0.6.
a.) Construct a decision tree. Compute the expected opportunity loss for each decision alternatives (i.e., draw a regret table).
b.) What is the expected value of perfect information?
c.) Because of the expense involved in developing the initial molds and acquiring the necessary equipment to produce fiberglass sailboats for young children, Monica has decided to conduct a pilot study before making any decisions to make sure that the market for the sailboats will be adequate. She estimates that the pilot study will cost her $10000. Furthermore, the pilot study can be either successful or not successful. Monica estimates that the probability of a successful pilot study, given a favorable market, is 0.9, while the probability of an unsuccessful pilot study, given an unfavorable market, is 0.8. Construct the associated decision tree. Do you recommend Monica to do the pilot study? What is the maximal amount Monica can accept to pay to the company making the pilot study?
d.) What is the expected value of sample information? What is the efficiency of sample information?