Question $3(35$ pts$)$: Ajet Airlines has designed its check$-$in system to function as follows: arriving

passengers form a single line and are served by the first available check$-$in staff on a first$-$come, first$-$

served basis. A total of $22$ staff members are assigned to the check$-$in counters. Passengers arrive at an

average rate of $4$ per minute, with an average check$-$in time of $5$ minutes per passenger. The standard

deviation for passenger interarrival time is $1$ minute, while the standard deviation for check$-$in

processing time is $10$ minutes. There are no group arrivals, ample waiting space is available for all

passengers, and no passengers abandon the line.