Janson's Department Store in Stark, Ohio, maintains a successful catalog sales department in which a clerk takes orders by telephone. If the clerk is occupied on one line, incoming phone calls to the catalog department are answered automatically by a recording machine and asked to wait. As soon as the clerk is free, the party who has waited the longest is transferred and serviced first. Calls come in at a rate of about $12$ per hour. The clerk can take an order in an average of $4\mathrm{.}0$ minutes. Calls tend to follow a Poisson distribution, and service times tend to be negative exponential.

The cost of the clerk is $$10$ per hour, but because of lost goodwill and sales, Janson's loses about $$25$ per hour of customer time spent waiting for the clerk to take an order.

a$)$ The average time that catalog customers must wait before their calls are transferred to the order clerk $=16$ minutes $($round your response to two decimal places$).$

b$)$ The average number of callers waiting to place an order $=3\mathrm{.}2$ callers $($round your response to two decimal places$).$

The present total cost per hour $($service cost $+$ waiting cost$)=$$$90$ per hour $($round your response to two decimal places$).$

c$)$ Janson's is considering adding a second clerk to take calls. The store's cost would be the same $$10$ per hour. The total cost $($service cost $+$ waiting cost$)=$$ per hour $($round your response to two decimal places$).$