Thomas Carter, manager of the Northstar hotel, is considering how to restructure the front desk to reach an optimum level of staff efficiency and guest service. At present, the hotel has $5$ servers on duty, each with a separate line served by a single server. During the peak check in hours of $3$:$00-5$:$00$ pm$,90$ customers arrive per hour with a $c_a$ of $1.$ It takes an average of $3$ minutes for the front desk clerk to register each guest with a $c_p$ of $1.$

What is the average number of people in the lobby $($both waiting and being served$)$ under the current configuration?

$11\mathrm{.}44$

$9\mathrm{.}00$

$45\mathrm{.}00$

$57\mathrm{.}21$