You have been asked to analyze the queue for registrations for a popular Financial 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 $$15$ per hour. It takes $6$ minutes to register a guest, following a $($negative exponential distribution$).$ The conference recognizes a waiting cost of $$55$ per hour per guest in line. $($The goal is to not have the attendees wait in line more than $6\mathrm{.}5$ minutes$).$