You have been asked to analyze the queue for registrations for a popular MSOM seminar at a major national conference. Conference attendees arrive to register at the rate of $3$ people every $12$ minutes $($Poisson distributed$).$ It takes each host, any number of which can be hired directly through the conference at the cost of $$15$ per hour, $6$ minutes to register a guest, following a negative exponential distribution. The conference recognizes a waiting cost of $$55$ per hour per guest in line. A single waiting line is set up$,$ but can accommodate multiple servers.