Average arrival rate of customers now has reached $20$ per hour and Sunset Airlines must increase the capacity of its check$-$in system. Based on a customer survey, $$15$ per hour is considered the opportunity cost of waiting in queue. Clerks are paid $$10$ per hour and still process a passenger in four minutes. Evaluate the following check$-$in system alternatives to find the least expensive arrangement using total hourly costs of clerks and customers waiting in queue. Assume that the average service time of the single clerk remains unchanged at $4$ minutes. Also, please remember that the formula for total cost is: TC $=$ Cs$*$C $+$ Cw$*$Lq

Instead of adding an additional server, consider adding one self$-$serve ATM $($Automatic Ticketing Machine$)$ with constant service time of three minutes to help a single clerk. Assume demand is equally divided between the single clerk and the ATM.

$($Hint: Use M$/$G$/1$ model with constant service time for ATM; Of course, the existing server system will continue to be an M$/$M$/1$ system$)$

What is the total hourly costs of this arrangement if the ATM operating costs are negligible?

$($Hint: Total Cost of system $=$ Cost for the M$/$M$/1$ system $+$ Cost of the ATM system$)$

Group of answer choices

$20\mathrm{.}25$

$21\mathrm{.}5$

$0\mathrm{.}05$

$15\mathrm{.}00$

$33\mathrm{.}75$

$21\mathrm{.}25$