A small bank is trying to determine how many tellers to employ. The total cost of employing a teller is $10 per hour, and a teller can serve an average of 120 customers per day. An average of 100 customers per day arrive at the bank, and both service times and interarrival times are exponential. If the delay cost per customer-hour is $10 and bank is working 8 hours per day, how many tellers should the bank hire?
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A small bank is trying to determine how many tellers to employ. The total cost of employing a teller is $10 per hour, and a teller can serve an average of 120 customers per day. An average of 100 customers per day arrive at the bank, and both service times and interarrival times are exponential. If the delay cost per customer- hour is $10 and bank is working 8 hours per day, how many tellers should the bank hire?
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- Currently, Commercial Banks have 1 unit of ATM machines to meet customer needs. It is known that there is an average of 15 customers in the system. Then it is also known that the average time spent by someone in the system is 10 minutes. Assume that the system follows M/M/1. The Commercial Bank operational manager is considering whether it is necessary to add 1 unit of ATM machine. What are your considerations? To strengthen the consideration, compare the queue length, queue length, and utilities before and after adding an ATM machine?During the early morning hours, customers arrive at a branch post office at an average rate of 45 per hour (Poisson), while clerks can handle transactions in an average time (exponential) of 4 minutes each. Find: (a) The average number of customers waiting for service if 5 clerks are used. (b) The minimum number of clerks needed to keep the average waiting time in the system to under 5 minutes. (c) If clerk cost is $40 per hour and customer waiting time represents a “cost” of $30 per hour, how many clerks can be justified on a cost basis? Please show work.Currently, Commercial Banks have 1 unit of ATM machines to meet customer needs. It is known that there is an average of 12+x customers in the system. Then it is also known that the average time spent by someone in the system is 10 minutes. Assume that the system follows M/M/1. The Commercial Bank operational manager is considering whether it is necessary to add 1 unit of ATM machine. What are your considerations? To strengthen the consideration, compare the queue length, queue length, and utilities before and after adding an ATM machine? Note: x denoted by the last number of my ID Number.Example, if my ID number is 2602296545, then the number used are “5”
- Consider a bank with two tellers. An average of 2 customers per hour arrive at the bank and wait in a single línea for an idle teller. The average time it takes to serve a customer is triangular (x1=1, y1=0), (x2=4, y2=2/3) Assume that inter-arrival times and services time is exponential. Develop the service (ST) equation? a. Y=2x-22/6B. Y=2x-22/3C. Y=22/3x-2/3D. Y=2x-3/22The Corner Cleaners 24-hour laundromat has 16 washing machines. A machine breaks down every 20 days(exponentially distributed). The repair service the laundromat contracts takes an average of one day to repair amachine (exponentially distributed). A washing machineaverages $5 per hour in revenue. The laundromat is considering a new repair service that guarantees repairs in0.50 day, but they charge $10 more per hour than thecurrent repair service. Should the laundromat switch tothe new repair service?Neve Commercial Bank is the only bank in the town of York, Pennsylvania. On a typical Friday, an average of 10 customers per hour arrive at the bank to transact business. There is currently one teller at the bank, and the average time required to transact business is 4 minutes. It is assumed that service times may be described by the negative exponential distribution. If asingle teller is used, find:a) The average time in the line.b) The average number in the line.c) The average time in the system.d) The average number in the system.e) The probability that the bank is empty.f)CEO Benjamin Neve is considering adding a second teller (who would work at the same rate as the first) to reduce the waiting time for customers. A single line would be used, and the customer at the front of the line would go to the first available bank teller. He assumes that this will cut the waiting time in half. If a second teller is added, find the new answers to parts (a) to (e).