First Local Bank would like to Improve customer service at lis drive$-$In facility by reducing

wailing and transaction times. On the basis of a pilot study, the bank's process manager

estimates the average rate of customer arrival is $30$ per hour. All arriving cars line up

in a single queue and are served at one of four windows on the first$-$come$/$first$-$serve

basis. Each teller currently requires an average of $6$ minutes to complete a customer

transaction. Assume that inter$-$arrival and activity times are exponentially distributed.

The bank is considering the possibility of leasing high$-$speed information retrieval and

communication equipment that would cost $$30$ per hour. The new equipment would,

however, serve the entire facility and reduce each teller's transaction processing time

to an average of $4$ minutes per customer. If our manager estimates that the cost of

customer's waiting time in queue $($in terms of future business lost to the competition$)$ to

be $$20$ per customer per hour, can he justify leasing the new equipment on an economic

basis?

Please explain the solution process and show your solution.