First Local bank would like to enhance customer service at its drive in facility by decreasing waiting and transaction times. One the basis of pilot study, banks process manager evaluates 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 first come fist served basis. Each teller presently needs average of 6 minutes to complete transaction. Bank is thinking of possibility of leasing high speed information retrieval and communication equipment which would cost $30 per hour. New equipment would though serve entire facility and decrease each tellers transaction processing time to average of 4 minutes per customer. Suppse that interarrival and activity times are exponentially distributed.
If our manager evaluates cost of a customers waiting time in queue in terms of future business lost to competition to be $20 per customer per hour can she describe leasing new equipment on economic basis?
Though waiting cost figure of $20 per customer per hour appears problemable, casual study of competition points out that customer must be in and out of drive in facility within average of 8 minutes including waiting time. If first local wishes to meet this standard must it lease new high speed equipment?