Reference no: EM133357052

Repairs of MTA buses: The metropolitan transit authority of a region wishes to establish a crew of auto mechanics that will be responsible for repairing the authority's buses. The crew is stationed at a single location. Bus breakdowns occur randomly (Poisson process) at a mean rate of one per hour. The time required to fix a bus has an exponential distribution (regardless of crew size). The expected repair time required by a one-worker crew would be 2 hours. The cost per hour for each member of a repair crew is $10.00. The cost that is attributable to not having a bus in use (i.e., a bus standing at the bus repair shop) is estimated to be $40.00 per hour (if a bus is not in use for half an hour, the cost would be $20 for example). Both men and buses are on 8-hour days. Assume that the mean service rate of the repair crew is proportional to its size (e.g., the service rate of a crew with two members would be twice as large as that of a crew with one member). What should the crew size be in order to minimize the expected total cost of this operation per hour?