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Willow Brook National Bank operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cars. On weekday mornings, arrivals to the drive-up teller window occur at random, with an arrival rate of 30 customers per hour or 0.5 customers per minute. In the same bank waiting line system, assume that the service times for the drive-up teller follow an exponential probability distribution with a service rate of 36 customers per hour, or 0.6 customers per minute. Determine the following operating characteristics for the system: a. The probability that no customers are in the system. If required, round your answer to four decimal places. Po = b. The average number of customers waiting. If required, round your answer to four decimal places. Lg= c. The average number of customers in the system. If required, round your answer to nearest whole number. L = d. The average time a customer spends waiting. If required, round your answer to four decimal places. Wq = e. The average time a customer spends in the system. If required, round your answer to nearest whole number. min

Willow Brook National Bank operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cars. On weekday mornings, arrivals to the drive-up teller window occur at random, with an arrival rate of 30 customers per hour or 0.5 customers per minute. In the same bank waiting line system, assume that the service times for the drive-up teller follow an exponential probability distribution with a service rate of 36 customers per hour, or 0.6 customers per minute. Determine the following operating characteristics for the system: a. The probability that no customers are in the system. If required, round your answer to four decimal places. Po = b. The average number of customers waiting. If required, round your answer to four decimal places. Lg= c. The average number of customers in the system. If required, round your answer to nearest whole number. L = d. The average time a customer spends waiting. If required, round your answer to four decimal places. Wq = e. The average time a customer spends in the system. If required, round your answer to nearest whole number. min

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Willow Brook National Bank operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cars. On weekday mornings, arrivals to the drive-up teller window occur at random, with an arrival rate of 30 customers per hour or 0.5 customers per minute. In the same bank waiting line system, assume that the service times for the drive-up teller follow an exponential probability distribution with a service rate of 36 customers per hour, or 0.6 customers per minute. Determine the following operating characteristics for the system: a. The probability that no customers are in the system. If required, round your answer to four decimal places. Po = b. The average number of customers waiting. If required, round your answer to four decimal places. Lq = c. The average number of customers in the system. If required, round your answer to nearest whole number. L = d. The average time a customer spends waiting. If required, round your answer to four decimal places. Wq = e. The average time a customer spends in the system. If required, round your answer to nearest whole number. W = min Pw= min f. The probability that arriving customers will have to wait for service. If required, round your answer to four decimal places.
Transcribed Image Text:Willow Brook National Bank operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cars. On weekday mornings, arrivals to the drive-up teller window occur at random, with an arrival rate of 30 customers per hour or 0.5 customers per minute. In the same bank waiting line system, assume that the service times for the drive-up teller follow an exponential probability distribution with a service rate of 36 customers per hour, or 0.6 customers per minute. Determine the following operating characteristics for the system: a. The probability that no customers are in the system. If required, round your answer to four decimal places. Po = b. The average number of customers waiting. If required, round your answer to four decimal places. Lq = c. The average number of customers in the system. If required, round your answer to nearest whole number. L = d. The average time a customer spends waiting. If required, round your answer to four decimal places. Wq = e. The average time a customer spends in the system. If required, round your answer to nearest whole number. W = min Pw= min f. The probability that arriving customers will have to wait for service. If required, round your answer to four decimal places.
Ocala Software Systems operates a technical support center for its software customers. If customers have installation or use problems with Ocala software products, they may telephone the technical support center and obtain free consultation. Currently, Ocala operates its support center with one consultant. If the consultant is busy when a new customer call arrives, the customer hears a recorded message stating that all consultants are currently busy with other customers. The customer is then asked to hold and is told that a consultant will provide assistance as soon as possible. The customer calls follow a Poisson probability distribution, with an arrival rate of five calls per hour. On average, it takes 10.5 minutes for a consultant to answer a customer's questions. The service time follows an exponential probability distribution. To improve customer service, Ocala Software Systems wants to investigate the effect of using a second consultant at its technical support center. What effect would the additional consultant have on customer service? Would two technical consultants enable Ocala to meet its service guidelines (no more than 35% of all customers having to wait for technical support and an average customer waiting time of two minutes or less)? Round your answers to two decimal places. With two consultants, Therefore, two consultants | % of customers have to wait, with an average waiting time of service goals. meet do not meet ● Agan Interior Design provides home and office decorating assistance to its customers. In normal operation, an average of 2.1 customers arrive each hour. One design consultant is available to answer customer questions and make product recommendations. Agan's management would like to evaluate two alternatives: Use one consultant with an average service time of 8 minutes per customer. • Expand to two consultants, each of whom has an average service time of 10 minutes per customer. minutes. If the consultants are paid $16 per hour and the customer waiting time is valued at $23 per hour for waiting time prior to service, should Agan expand to the two-consultant system? Yes or No What is the total cost for each scenario? Round your answers to the nearest cent. The total cost for the first scenario where there is one consultant with an average service time of 8 minutes per customer is $ The total cost for the second scenario where there are two consultants with an average service time of 10 minutes per customer is $
Transcribed Image Text:Ocala Software Systems operates a technical support center for its software customers. If customers have installation or use problems with Ocala software products, they may telephone the technical support center and obtain free consultation. Currently, Ocala operates its support center with one consultant. If the consultant is busy when a new customer call arrives, the customer hears a recorded message stating that all consultants are currently busy with other customers. The customer is then asked to hold and is told that a consultant will provide assistance as soon as possible. The customer calls follow a Poisson probability distribution, with an arrival rate of five calls per hour. On average, it takes 10.5 minutes for a consultant to answer a customer's questions. The service time follows an exponential probability distribution. To improve customer service, Ocala Software Systems wants to investigate the effect of using a second consultant at its technical support center. What effect would the additional consultant have on customer service? Would two technical consultants enable Ocala to meet its service guidelines (no more than 35% of all customers having to wait for technical support and an average customer waiting time of two minutes or less)? Round your answers to two decimal places. With two consultants, Therefore, two consultants | % of customers have to wait, with an average waiting time of service goals. meet do not meet ● Agan Interior Design provides home and office decorating assistance to its customers. In normal operation, an average of 2.1 customers arrive each hour. One design consultant is available to answer customer questions and make product recommendations. Agan's management would like to evaluate two alternatives: Use one consultant with an average service time of 8 minutes per customer. • Expand to two consultants, each of whom has an average service time of 10 minutes per customer. minutes. If the consultants are paid $16 per hour and the customer waiting time is valued at $23 per hour for waiting time prior to service, should Agan expand to the two-consultant system? Yes or No What is the total cost for each scenario? Round your answers to the nearest cent. The total cost for the first scenario where there is one consultant with an average service time of 8 minutes per customer is $ The total cost for the second scenario where there are two consultants with an average service time of 10 minutes per customer is $
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