1. Draw a decision tree to represent this problem.

2. Calculate the total value at each endpoint.

3. Solve the decision tree and summarize the optimal decision strategy

4. Suppose that the engineer is unsure of her estimate of there being a 50% chance that she could fix the machine herself in 5 days. Conduct a sensitivity analysis on that estimate. What does the result of that analysis tell you?

A large machine in a factory has broken down and the company that owns the factory will incur costs of $3000 for every day the machine is out of service. The factory’s engineer has three immediate options: Option 1: She can return the machine to the supplier who has agreed to collect, repair, and return it free of charge, but not to compensate the company for any losses they might incur while the repair is being carried out. The supplier will not agree to repair the machine if any other person has previously attempted to repair it. If the machine is returned, the supplier will guarantee to return it in working order in 10 days’ time. Option 2: She can call in a specialist local engineering company. They will charge $20,000 to carry out the repair, and they estimate that there is a 30% chance that they will be able to return the machine to working order in 2 days. 

There is, however, a 70% chance that repairs will take 4 days. Option 3: She can attempt carry out the repair work herself, and she estimates that there is a 50% chance that she could mend the machine in 5 days. However, if at the end of 5 days the attempted repair has not been successful, she will then have to decide whether to call in the local engineering company or to make a second attempt at repair by investigating a different part of the mechanism. This would take two further days, and she estimates that there is a 25% chance that this second attempt would be successful. If she fails at the second attempt, she will have no alternative other than to call in the local engineering company.

Answer rating: 100% (QA)

1 and 2 Decision tree 3 The optimal decision is to try it i... View the full answer