A supermarket manager is trying to decide how many cashers to employ for the peak time. The service times for check outs are exponentially distributed with a mean service time of 4 minutes. Customer arrivals to cashiers follow a Poisson arrival process with an average 54 customers per hour.
(a) What is the minimum number of cashers that would be needed to have the utilization less than one?
(b) What is the minimum number of cashers that would be needed to assure that the average waiting time is less than 2 minutes?