A large machine in a factory has broken down and the company that owns the factory will incur costs of $3200 for each day the machine is out of action. The factory’s engineer has three immediate options:

Option 1

He 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

He 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

He can attempt to carry out the repair work himself, and he estimates that there is a 50% chance that he could mend the machine in 5 days. However, if at the end of 5 days the attempted repair has not been successful he will 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 2 further days, and he estimates that there is a 25% chance that this second attempt would be successful. If he fails at the second attempt, he will have no alternative other than to call in the local engineering company. It can be assumed that the probability distribution for the local engineering company’s repair time will be unaffected by any work which the factory engineer has carried out.

Assuming that the engineer’s objective is to minimize expected costs, what course(s