The management of Dream Cruises, Ltd., operating in the Caribbean, has established the need for expanding its fleet capacity and is considering what the best plan for the next 8-year planning period will be. One strategy is to buy a larger 40,000-ton cruise ship now, which would be most profitable if demand is high. Another strategy would be to start with a small 15,000-ton ship now and consider buying another medium 25,000-ton ship 3 years later. The planning department has estimated the probabilities for high and low demand for each period to be 0.6 and 0.4. If the company buys the large ship, then the annual profit after taxes for the next 8 years is estimated to be $800,000 if demand is high and $100,000 if it is low. If the company buys the small ship, then the annual profits each year will be $300,000 if demand is high and $150,000 if it is low. 

After 3 years with the small vessel, a decision for new capacity will be reviewed. At this time, the firm may decide to expand by adding a 25,000-ton ship or by continuing with the small one. The annual profit after expansion will be $700,000 if demand is high and $120,000 if it is low. 

a. Prepare a decision tree that shows the actions available, the states of nature, and the annual profits. 

b. Calculate the total expected profit for each branch in the decision tree covering 8 years of operation. 

c. Determine the optimum fleet-expansion strategy for Dream Cruises, Ltd.