The registration area has just opened at a large convention of dentists in Tallahassee, Florida. One hundred dentists arrive per hour $($Poisson distributed$),$ and the cost of their waiting time in the queue is valued at $$150$ per person per hour. The Tallahassee Convention Center provides servers to register guests at a fee of $$12$ per person per hour. It takes about one minute to register an attendee $($negative exponentially distributed$).$ A single waiting line, with multiple servers, is set up$.$

What is the minimum number of servers for this system? $[$ Select $]["3","1","2","4"]$

a$.$ What is the optimal number of servers for this system based on evaluating waiting cost? $[$ Select $]["1","2","4","3"]$

b$.$ What is the cost waiting cost, per hour, at the optimum number of servers? $[$ Select $]["$$$58\mathrm{.}98","$$$312\mathrm{.}27","$$$308\mathrm{.}98","$$$62\mathrm{.}27"]$

c$.$ What is the down time per server at the minimum number of servers? $[$ Select $]["9\mathrm{.}1\%","33\%","83\%","18\mathrm{.}8\%"]$

d$.$ Based on the minimum number of servers, what is the average time that an attendee has to wait before being checked in$,$ based on the number of minutes? $[$ Select $]["3\mathrm{.}27$ minutes", $"2\mathrm{.}27$ minutes", $"2\mathrm{.}63$ seconds", $"\mathrm{.}04$ of a minute"$]$