4.3 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 a negative 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. (Both men and buses are on 8-hour days.)
        Assume that the mean service rate of the repair crew is proportional to its size. What should the crew size be in order to minimize the expected total cost of this operation per hour? Repeat this question but with the mean service rate proportional to the square root of the crew size.