Bob is an apartment complex manager. Recently, he has received complaints from tenants that the washer/dryer in his unit is not working properly. The complex will be completely remodeled three years from now, and therefore, he is considering the following three temporary solutions until then:
1) Purchase a new washer/dryer. He can purchase a new one for $400, and it will easily last three years.
2) Repair the current one. The repair costs $150, and he also believes that there is only a 30 percent chance that it will last a full three years after repairing. If the repaired washer/dryer does not last three years, he will have to buy a new one ($400).
3) Purchase a used washer/dryer. This costs $200, and he estimates that there is a 60% probability that it will last at least three years. If it breaks down, he will have the option of repairing it for $150 or buying a new one. If he repairs, there is a 30 percent chance that it will last. If it doesn’t he will have to buy a new one.
a) Construct a decision tree for this problem. Please be sure to label all nodes and branches clearly.
b) Identify the strategy that minimizes Bob’s expected cost for the next three years. Describe all the contingency plans. For instance, “buy a used washer/dryer” is not a complete answer. What is the expected cost?