Problem 33 Someone Help Answer Question Set Excel Part National Bank Union County Bank Sma Q29598540

Problem 3.3

Can someone help me answer this question and set it up inexcel?

PART A:   The NationalBank of Union County is the only bank in the small town of Cove,Oregon. On a typical Friday, an average of 10 customers arrive perhour (Poisson distributed) to transact business. There is only oneteller in the bank, and the average time to transact business is 5minutes (exponentially distributed). Although this is the only bankin town, the delays at the bank have caused some people to use thesavings and loan in the city of Imbler, some twenty miles away.Given this scenario, find:

a.) The average time in the line, in minutes;

b.) The average number of people waiting in the line;

c.)The average time it takes to transact business in minutes,from the time one enters the bank until their business has beenconcluded;

d.) The average number of people in the line, including theperson being served;

e.) The probability that someone is in the system;

f.) The probability that no one will be in line;

g.) The probability that there are five or more people thesystem.

PART B:   The salary andbenefits for a teller at Union County Bank is $12 per hour. Thebank is open 8 hours per day. It has been estimated that thewaiting time cost is $25 per hour in the line. Using thisinformation and the data for the two teller system provided below,determine:

h.) How many customers enter the bank on a given day?

i.) How much total time would the customers spend waiting inline during an entire day if one teller is working? What is thetotal daily waiting time cost? (Use Wq in your formulas.)

j.) How much total time would the customers spend waiting inline during an entire day if two tellers were working? What is thetotal waiting time cost? (Use Wq in your formulas.)

k.) If the bank manager wishes to minimize personnel costs andsystem costs, how many tellers should be used? Explain yourrationale using cost formulas to justify your response.

Two tellers: Arrival rate ()10 Service rate (?- 12 customers per hour customers per hour Number of Servers2 Average time in the queue (Wq)1.0504 Average number in the queue (Lq)0.1751 Average time in the system (W)6.0504 Average number in the system(L)-1.0084 Utilization (p) 0.4167 P(o)0.4118 0.2451 0.0103 minutes customers minutes customers Probability that there will be a wait (Pw) Probability of 5 in the system (Pn) calculated for more than 4 Show transcribed image text