Answer all steps in detail, show all work

$3.$ Nickel$-$Rent$-$A$-$Car, an auto rental company, has $2$ agents staffing their rental operation at their SEA$-$TAC airport counter. Approximately, $30\backslash \%$ of the arrivals hold Nickel $-$Rent$-$A$-$Car Express membership card, and the rest are general public customers. It is estimated that the arrivals are Poisson with a mean rate of $25$ per hour. Currently, a feeder$-$line is being employed where all customers form a single line and are served on a First Come First Served basis. The time a customer spends at the counter with an agent is exponentially distributed with a mean of $4\mathrm{.}5$ minutes. Nickel$-$Rent$-$A$-$Car estimates the waiting cost in the queue for member and general customers at $\backslash (\backslash$$ $0\mathrm{.}6\backslash )$ and $\backslash (\backslash$$ $0\mathrm{.}2\backslash )$ per minute, respectively.

a$)$ Identify the queueing system associated with the operation and find the average total cost per hour of the operation.

b$)$ Suppose the management is considering a proposal to create two separate lines, one for the members, and another for the general public customers. In this situation, each line will have one staff who will serve their respective customers. However, the service times will change under this setting. That is$,$ the average service time for the member and general queues will be $2$ and $3$ minutes, respectively $($service distribution will be exponential, as before$).$ Identify the queueing system associated with this configuration, find the average total hourly cost associated with this configuration, and conclude whether management should adopt this proposal