$[($Waiting at PoliBurger$)$ This and next $3$ questions refer to the following: Jim, the manager of PoliBurger $($a fast$-$food hamburger restaurant$),$ learns from his experience that it is a key to the success of the restaurant to provide fast service is$.$ Customers who have to wait very long are likely to go to one of the other nearby fast$-$food restaurants next time. He estimates that each minute a customer has to wait in line before completing service costs him an average of HK$$1\mathrm{.}80$ in lost future business. Therefore, he wants to be sure that enough cashiers always are open to keep waiting to a minimum. Each cashier is operated by a part$-$time employee who obtains the food ordered by each customer and collects the payment. The total cost for each such employee is $$54$ per hour. $///$ During lunchtime, customers arrive randomly at a mean rate of $66$ per hour. The time needed to serve a customer is estimated to have an exponential distribution with a mean of two minutes.$]$ What is the service rate $($per hour$)$ of a cashier?