EBK PRODUCTION AND OPERATIONS ANALYSIS
7th Edition
ISBN: 8220102480681
Author: Olsen
Publisher: WAVELAND
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A cafeteria serving line has a coffee urn from which customers serve themselves. Arrivals at the urn follow a Poisson distribution at the rate of 4.0 per minute. In serving themselves, customers take about 11 seconds, exponentially distributed.
a. How many customers would you expect to see on the average at the coffee urn?
b. How long would you expect it to take to get a cup of coffee?
c. What percentage of time is the urn being used?
d. What is the probability that three or more people are in the cafeteria?
e. If the cafeteria installs an automatic vendor that dispenses a cup of coffee at a constant time of 11 seconds, how many customers would you expect to see at the coffee urn (waiting and/or pouring coffee)?
f.If the cafeteria installs an automatic vendor that dispenses a cup of coffee at a constant time of 11 seconds, how long would you expect it to take (in minutes) to get a cup of coffee, including waiting time?
A university is considering setting up an information desk manned by one employee. Based on information obtained from similar information desks, it is believed that people will arrive at the desk at the rate of 18 per hour. It takes an average of 2 minutes to answer a question. It is assumed that arrivals are Poisson and answer times are exponentially distributed.
3. Find the proportion of the time that the employee is busy.
4. Find the average number of people receiving and waiting to receive information.
5. Find the average number of people waiting in line to get information.
Quick Oil provides a single-channel automobile oil change and lubrication service.Customers provide an arrival rate of 4 cars per hour. The service rate is 5 cars perhour. Assume that arrivals follow a Poisson probability distribution and that servicetimes follow an exponential probability distribution.
a. What is the average number of cars in the system?
b. What is the average time that a car waits for the oil and lubrication serviceto begin?
c. What is the probability that an arrival has to wait for service?
*Please solve for a-c typing or neatly writing all your work/steps and answers on paper, NO EXCEL* thank you !
Chapter 7 Solutions
EBK PRODUCTION AND OPERATIONS ANALYSIS
Ch. 7.1 - Prob. 1PCh. 7.1 - Prob. 2PCh. 7.1 - Prob. 3PCh. 7.1 - Prob. 4PCh. 7.1 - Prob. 5PCh. 7.1 - Prob. 6PCh. 7.1 - Prob. 7PCh. 7.2 - Prob. 8PCh. 7.2 - Prob. 9PCh. 7.2 - Prob. 10P
Ch. 7.3 - Prob. 11PCh. 7.3 - Prob. 12PCh. 7.3 - Prob. 13PCh. 7.3 - Prob. 14PCh. 7.3 - Prob. 15PCh. 7.3 - Prob. 16PCh. 7.3 - Prob. 18PCh. 7.4 - Prob. 19PCh. 7.4 - Prob. 21PCh. 7.4 - Prob. 22PCh. 7.4 - Prob. 23PCh. 7.5 - Prob. 24PCh. 7.5 - Prob. 25PCh. 7.5 - Prob. 26PCh. 7.5 - Prob. 27PCh. 7.8 - Prob. 28PCh. 7.8 - Prob. 29PCh. 7.8 - Prob. 30PCh. 7.8 - Prob. 32PCh. 7.8 - Prob. 34PCh. 7.8 - Prob. 35PCh. 7.8 - Prob. 36PCh. 7 - Prob. 38APCh. 7 - Prob. 39APCh. 7 - Prob. 40APCh. 7 - Prob. 41APCh. 7 - Prob. 42APCh. 7 - Prob. 43APCh. 7 - Prob. 44APCh. 7 - Prob. 45APCh. 7 - Prob. 46AP
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- Suppose that arrivals to a hairdresser follow a Poisson process with mean 12 customers per hour. Calculate the probabilities of: a) no customers in 20 minutes; b) exactly one customer in 5 minutes; c) exactly 12 customers in a hour; d) fewer than three customers in 10 minutes.arrow_forward6. The Security & Trust Bank employs 4 tellers to serve its customers. Customers arrive according to a Poisson process at a mean rate of 2 per minute. However, business is growing and management projects that the mean arrival rate will be 3 per minute a year from now. The transaction time between the teller and customer has an exponential distribution with a mean of 1 minute. Management has established the following guidelines for a satisfactory level of service to customers. The average number of customers waiting in line to begin service should not exceed 1. At least 90 percent of the time, the number of customers waiting in line should not exceed 3. a)Use the Excel sheet to determine how many tellers will be needed a year from now to completely satisfy these guidelines.arrow_forward6. The Security & Trust Bank employs 4 tellers to serve its customers. Customers arrive according to a Poisson process at a mean rate of 2 per minute. However, business is growing and management projects that the mean arrival rate will be 3 per minute a year from now. The transaction time between the teller and customer has an exponential distribution with a mean of 1 minute. Management has established the following guidelines for a satisfactory level of service to customers. The average number of customers waiting in line to begin service should not exceed 1. At least 90 percent of the time, the number of customers waiting in line should not exceed 3. (a) Use the Excel sheet to evaluate how well the guidelines will be satisfied a year from now if no change is made in the number of tellers.arrow_forward
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