$4.$ The registration area has just opened at a large convention center. There are $80$ people arriving per hour $($Poisson distributed$),$ and the cost of their waiting time in queue is valued at $$50$ per person per hour. The convention center pays $$30$ per hour per server to register guests. It takes about two minutes to register an attendee $($exponentially distributed$).$ A single waiting line, with multiple servers, is set up: