The average number of mechanics at counter those being served.

Question

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Answer 1

Question

Chapter 18, Problem 8P

a.

Summary Introduction

To determine: The average number of mechanics at counter those being served.

b.

Summary Introduction

To determine: The probability that mechanics will have to wait.

c.

Summary Introduction

To determine: How long mechanics will have to wait.

d.

Summary Introduction

To determine: The percentage of idle time.

e.

Summary Introduction

To determine: The optimal number of clerk minimizing total cost.

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Students have asked these similar questions

The parts department of a large automobile dealership has a counter used exclusively for mechanics’ requests for parts. The time between requests can be modeled by a negative exponential distribution that has a mean of five minutes. A clerk can handle requests at a rate of 15 per hour, andthis can be modeled by a Poisson distribution that has a mean of 15. Suppose there are two clerksat the counter.a. On average, how many mechanics would be at the counter, including those being served?b. What is the probability that a mechanic would have to wait for service?c. If a mechanic has to wait, how long would the average wait be?d. What percentage of time are the clerks idle?e. If clerks represent a cost of $20 per hour and mechanics a cost of $30 per hour, what numberof clerks would be optimal in terms of minimizing total cost?

Zimmerman’s Bank is the only bank in the small town of St. Thomas. On a typical Friday, an average of 10 customers per hour arrive at the bank to transact business. There is 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 exponential distribution. A single line would be used, and the customer at the front of the line would go to the first available bank teller. If a single teller is used, find: The average time in the line. The average number in the line. The average time in the system. The average number in the system. The probability that the bank is empty.

The office has a single line for customers waiting for the next available clerk. There are two clerks who work at the same rate. On average customers arrive every 8 minutes and the average service rate is 5 per hour for each of the two clerks. The arrival rate of customers follows a Poisson distribution, while the service time follows an exponential distribution. b.) What proportion of time are both clerks idle? c.) Counting each person being served and the people in line, on average, how many customers would be in this system?

Answer 2

Question

Chapter 18, Problem 8P

a.

Summary Introduction

To determine: The average number of mechanics at counter those being served.

b.

Summary Introduction

To determine: The probability that mechanics will have to wait.

c.

Summary Introduction

To determine: How long mechanics will have to wait.

d.

Summary Introduction

To determine: The percentage of idle time.

e.

Summary Introduction

To determine: The optimal number of clerk minimizing total cost.

Expert Solution & Answer

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Answer 3

Question

Chapter 18, Problem 8P

a.

Summary Introduction

To determine: The average number of mechanics at counter those being served.

b.

Summary Introduction

To determine: The probability that mechanics will have to wait.

c.

Summary Introduction

To determine: How long mechanics will have to wait.

d.

Summary Introduction

To determine: The percentage of idle time.

e.

Summary Introduction

To determine: The optimal number of clerk minimizing total cost.

Expert Solution & Answer

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Answer 4

Question

Chapter 18, Problem 8P

a.

Summary Introduction

To determine: The average number of mechanics at counter those being served.

b.

Summary Introduction

To determine: The probability that mechanics will have to wait.

c.

Summary Introduction

To determine: How long mechanics will have to wait.

d.

Summary Introduction

To determine: The percentage of idle time.

e.

Summary Introduction

To determine: The optimal number of clerk minimizing total cost.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 18, Problem 8P

a.

Summary Introduction

To determine: The average number of mechanics at counter those being served.

b.

Summary Introduction

To determine: The probability that mechanics will have to wait.

c.

Summary Introduction

To determine: How long mechanics will have to wait.

d.

Summary Introduction

To determine: The percentage of idle time.

e.

Summary Introduction

To determine: The optimal number of clerk minimizing total cost.

Answer 6

Chapter 18, Problem 8P

a.

Summary Introduction

To determine: The average number of mechanics at counter those being served.

Answer 7

Chapter 18, Problem 8P

a.

Summary Introduction

To determine: The average number of mechanics at counter those being served.

Answer 8

b.

Summary Introduction

To determine: The probability that mechanics will have to wait.

Answer 9

b.

Summary Introduction

To determine: The probability that mechanics will have to wait.

Answer 10

c.

Summary Introduction

To determine: How long mechanics will have to wait.

Answer 11

c.

Summary Introduction

To determine: How long mechanics will have to wait.

Answer 12

d.

Summary Introduction

To determine: The percentage of idle time.

Answer 13

d.

Summary Introduction

To determine: The percentage of idle time.

Answer 14

e.

Summary Introduction

To determine: The optimal number of clerk minimizing total cost.

Answer 15

e.

Summary Introduction

To determine: The optimal number of clerk minimizing total cost.

Answer 16

Expert Solution & Answer

Answer 17

Expert Solution & Answer

Answer 18

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Answer 19

Ch. 18.1 - Prob. 1.1RQ Ch. 18.1 - Prob. 1.2RQ Ch. 18 - Prob. 1DRQ Ch. 18 - Why do waiting lines form even though a service...Ch. 18 - Prob. 3DRQ Ch. 18 - Prob. 4DRQ Ch. 18 - What approaches do supermarkets use to offset...Ch. 18 - Prob. 6DRQ Ch. 18 - Prob. 7DRQ Ch. 18 - Prob. 8DRQ

The average number of mechanics at counter those being served.

Solution Summary: The author explains that the average number of mechanics at counter those being served is 0.952.

Concept explainers

To determine: The average number of mechanics at counter those being served.

To determine: The probability that mechanics will have to wait.

To determine: How long mechanics will have to wait.

To determine: The percentage of idle time.

To determine: The optimal number of clerk minimizing total cost.

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Chapter 18 Solutions