The registration area has just opened at a large convention of building contractors in Las Vegas. There are $200$ people arriving per hour $($time between arrivals is exponentially distributed$)$ and the cost of their time spent waiting in line and registering is valued at $$100$ per person per hour. The Las Vegas Convention Bureau provides workers to register guests at a cost of $$15$ per worker per hour. It takes on average one minute to register an attendee $($exponentially distributed$).$ A single waiting line with multiple workers will be set up$.$ What is the optimal number of workers to staff the registration area?