2. A bank has one drive-up teller. The teller can serve at the rate of 10.5 bank
ID: 3148440 • Letter: 2
Question
2. A bank has one drive-up teller. The teller can serve at the rate of 10.5 bank customers in an hour. Customers arrive at the drive-up window on an average every 7.5 minutes. The bank is currently analyzing the possibility of adding a second drive-up window at an annual cost of $18,000. It is assumed that arriving cars would be equally divided between both windows. It is estimated that each minute's reduction in customer waiting time would increase the bank's revenue by $2,400 annually. What will be net change in the bank's revenue? Should the second drive-up window be installed? Note: Do hand calculations to answer this question. Show all details of your answer.Explanation / Answer
given server rate m =10.5 bank customers /hour
Customers arrive at the drive up window on an average every 7.5 minutes
arrival rate L=60/7.5= 8customers per hour
before installing second drive
Utilization p=l/m=8/10.5=0.76=76%
Arrival rate Wq=l/m(m-l)
waiting time Wq=8/(10.5(10.5-8))=0.304761905
after installation waiting time Wq=4/10.5(10.5-4)=0.0586080586hour
reduction in waiting=0.304761905-0.0586080586=0.246153846*60=14.7692308mintues
by installing it makes a profit of 2400 per mintue for 14.7692308 min it makes a profit of 35446.1539
the bank should go fro the installation of second teller
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