First Local Bank would like to improve customer service at its drive-in facility by reducing waiting and transaction times. On the basis of a pilot study, the banks process manager estimates the average rate of customer arrivals at 15 per hour. All arriving cars line up in a single file and are served at a window on a first-come, first-served basis. Each transaction requires on average 3 minutes to complete. The bank is considering the possibility of leasing high-speed information-retrieval and communication equipment that would cost $20 an hour. The new equipment would reduce the average transaction time by one minute. Assume that the arrival process of cars (or customers) at the service window follows a Poisson process, and that the transaction times are exponentially distributed.

The customer relations manager estimates that the cost (loss of goodwill and future business, etc.) due to a customers waiting in queue has a fixed-plus-linear form, i.e., if a customer has to wait in line, then the bank incurs a cost equal to (2 + 10 x) dollars, where x is the time, in hours, the customer spends in queue. On the other hand, if a customer does not have to wait at all, the bank incurs zero cost.

1. In terms of total cost, should the bank lease the communications equipment? Please show the cost difference between the two scenarios (without the communication equipment and with the communication equipment) to justify your answer.

b) Another way to improve customer service is to open a second window and not lease the communications equipment. It costs $20 an hour to staff this window. The customers still form a single queue, and the service discipline is still first-come, first-served. Is this alternative better than the status quo? Is it better than the equipment-leasing option? Please use a cost analysis to justify your answer.