Question

A road transport company has one reservation clerk on duty at a time. He handles information on bus schedules and makes reservations. Customers arrive at a rate of 8 per hour, and the clerk can, on average, service 12 customers per hour. Find (a) the average number of customers waiting for the service of the clerk, (b) the average time a customer has to wait before being served, and (c) whether the management should install a computer for handling information and reservations. The installation of the computer is expected to reduce service time from 5 to 3 minutes. The additional cost of the system works out to Rs 50 per day. If the cost of goodwill of having to wait is 12 paise per minute spent waiting before being served, should the company install the computer? Assume an 8-hour working day.

          A road transport company has one reservation clerk on duty at a time. He handles information on bus schedules and makes reservations. Customers arrive at a rate of 8 per hour, and the clerk can, on average, service 12 customers per hour. Find (a) the average number of customers waiting for the service of the clerk, (b) the average time a customer has to wait before being served, and (c) whether the management should install a computer for handling information and reservations. The installation of the computer is expected to reduce service time from 5 to 3 minutes. The additional cost of the system works out to Rs 50 per day. If the cost of goodwill of having to wait is 12 paise per minute spent waiting before being served, should the company install the computer? Assume an 8-hour working day.

Show more…

Added by David C.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Supreeta N

03/31/2023

Step 1

(a) Show more…

Show all steps

lock

Thanks for your feedback!

A road transport company has one reservation clerk on duty at a time. He handles information on bus schedules and makes reservations. Customers arrive at a rate of 8 per hour, and the clerk can, on average, service 12 customers per hour. Find (a) the average number of customers waiting for the service of the clerk, (b) the average time a customer has to wait before being served, and (c) whether the management should install a computer for handling information and reservations. The installation of the computer is expected to reduce service time from 5 to 3 minutes. The additional cost of the system works out to Rs 50 per day. If the cost of goodwill of having to wait is 12 paise per minute spent waiting before being served, should the company install the computer? Assume an 8-hour working day.

Play audio

Feedback

Powered by NumerAI

Supreeta N and 70 other subject Intro Stats / AP Statistics educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Recommended Videos

Recommended Textbooks

Transcript

00:02 Hello student, according to the given question they have given lambda is equal to 8 per hour.

00:11 And here service time will be equal to 5 minutes.

00:17 So here the mu will be equal to 60 by 5 that is equal to 12 per hour.

00:25 So in the a bit the lh value will be lambda is divided by mu minus llllll.

00:32 Which is equal to 8 is divided by 12 minus 8 which is equal to 2.

00:39 So in the b bit here wq will be equal to lq by lambda.

00:46 Here lq will be equal to ls minus of lambda by mu.

00:51 That is equal to 2 minus of 8 by 12.

00:57 So which is equal to 4 by 3.

00:59 Here then wq will be 4 by 3 is divided by 8 which is equal to 1 by 6 per hour that is equal to 10 minutes.

01:12 In the c bit here average cost of a customer in system will be equal to 0 .12 rupees it is per minute.

01:31 So then wq here is equal to 10 minutes.

01:37 So therefore average average cost will be equal to 0 .12 into 10 that is equal to rupees 1 .20.

01:50 Here the arrival rate will be equal to 8 customers per hour.

01:58 So total number of customers in 8 hours that is equal to 8 so therefore here total cost of waiting will be equal to 64 into 1 .20 that is equal to 76 .80.

02:32 Here mu will be 60 is divided by 3 that is equal to 20...

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later