First Local bank would like to improve customer service at its drive in facility by reducing waiting and transaction times. One the basis of a pilot study, the banks process manager estimates the average rate of customer arrivals at 30 per hour. All arriving cars line up in single file and are served at 1 of 4 windows on a first come fist served basis. Each teller currently requires an average of 6 minutes to complete a transaction. The bank is considering the possibility of leasing high speed information retrieval and communication equipment that would cost $30 per hour. The new equipment would however serve the entire facility and reduce each tellers transaction processing time to an average of 4 minutes per customer. Assume that interarrival and activity times are exponentially distributed.

If our manager estimates the cost of a customers waiting time in queue in terms of future business lost to the competition to be $20 per customer per hour can she justify leasing the new equipment on an economic basis?

Although the waiting cost figure of $20 per customer per hour appears questionable, a casual study of the competition indicates that a customer should be in and out of a drive in facility within an average of 8 minutes including waiting time. If first local wants to meet this standard should it lease the new high speed equipment?