$11.$S$1.$ Managing Waiting Lines at First Bank

of Seattle

Sally Gordon completed her MBA degree a few years ago and

is proud to have earned a promotion to vice president for cus$-$

tomer services already at the First Bank of Seattle. One of her

responsibilities is to manage how tellers provide services to cus$-$

tomers. so she is taking a hard look at this area of the bank's

operations. Customers needing teller service arrive randomly at

a mean rate of $30$ per hour. Customers wait in a single line and

are served by the next available teller when they reach the front

of the line. Each service takes a variable amount of time $($assume

three minutes. The tellers earn an average wage of $$18$ per hour.

a$.$ If two tellers are used, what will be the average waiting time

for a customer before reaching a teller? On average, how

many customers will be in the bank, including those currently

being served?

b$.$ Company policy is to have no more than a $10$ percent chanot

that a customer will need to wait more than five minules $bx$ :

fore reaching a teller. How many tellers need to be used in

order to meet this standard?

c$.$ Sally feels that a significant cost is incurred by making A

customer wait because of potential lost future busines: