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SHRIRAMSWAROOPMEMORIALCOLLEGEOF ENGG. &MANAGEMENT

B.Tech. [SEM VII (ME)]

TUTORIAL SHEET-4(Session : 2011-12)

MECHANICAL SYSTEM DESIGN

(EME-043)Unit:IV Topic: System evaluation and optimization

Date of Distribution: Faculty Name: Ms Anupriya Saxena

1. A company produces four different designs of four pens. Their performance may be summarized as follows:

Determine which design gives the maximum utility.

2. What are simulation models ? how does simulation use the models to explore the nature of results?3. What is the role of random number in simulation activity ?4. A company has two plants to manufacture scooters. Plant I manufactures 70% scooters and plant II

manufactures 30%. AT plant I, 80% of scooters are rated standard quality. A scooter is picked up random

and is found to be standard quality. What is the chance that it has come from plant I or plant II?

5. A certain production process produces items that are 10% defective. Each item is inspected beforesupplying to customers but the inspector incorrectly classifies an item 10% of the time. Only item classified

as good are supplied.If 820 items have been supplied in all, how many of them are expected to be defective?

6. A newspaper distributor assigns probabilities to the demand for a magazine as follow:Copies demanded: 1 2 3 4

Probability .4 0.3 0.2 0.1

A copy of the magazine sells for Rs & and cost Rs 6. What can be the maximum possible expected EMVif the distributor can return unsold copies for Rs 5 each ?

7. The following pay off table is givenActs Events

E1 E2 E3 E4

A1 40 200 -200 100

A2 200 0 200 0

A3 0 100 0 150A4 -50 400 100 0

F:/Academic/27

Refer/WI/ACAD/18

Performance

parameter

Writing time

between refills

Nib life Cost Writing

pressure

A 35 24 10 .30

B 15 30 8 .20

C 65 20 20 .40

D 30 18 12 .25Min accepted value 10 15 20 .20

Weights .35 0.15 0.2 0.3

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Suppose that the probability of the events of this tables are p(E1)=0.20, p(E2)=0.15, p(E3)=0.40,

p(E4)=0.25, calculate the expected pay off and the expected loss of each action.

8. Telephone users arrive at a booth following a Poissons distribution with an average time of 5 minutebetween one arrival and next.The time taken for a telephone call is on an average 3 minutes and it follows

an exponential distribution. What is the probability that the booth is busy ?How many more booth should be

established to reduce the waiting time to less than or equal to half of the present waiting time?

9. A bakery keeps stock of popular brand of bread.Previous experience indicates the daily demand as givenbelow:

Daily demand : 0 10 20 30 40 50

Probability: 0.01 0.20 0.15 0.50 0.12 0.02

Consider the following sequence of random numbers:

48,78,19,51,56,77,15,14,68,9

Using the above sequence simulate the demand for the next 10 days.

i) Find out the stock situation if the owner of the bakery decides to make 30 breads every dayii) Estmate the daily average demand for the bread on the basis of simulated data.

10.What is the purpose of simulation? State its advantage and disadvantage.Supplementary Questions:

11.The automobile company manufactures around 150 scooters. The daily production varies from 146 to 154depending upon the availability of raw materials and other working conditions:

Production per day Probability

146 0.04

147 0.09

148 0.12

149 0.14

150 0.11

151 0.10

152 0.20

153 0.12

154 0.08

The finished scooters are transported in a specially arranged lorry accommodating 150 scooters. Using

following random numbers:

80,81,76,75,64,43,18,26,10,12,65,68,69,61,57 simulate the process to find out:

i)What will be the average number of scooters waiting in the factory?ii)What will be the average number of empty spaces on lorry?

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12.A bank plans to open a single server drive in banking facility at a particular center.It is estimated that 28customers will arrive each hour on an average.If, on an average it requires 2 minutes to process a customer

transaction, determine:

i) The protion of the time the system will be idle.ii) On the average , how long the customer will have to wait before reaching the server?iii) The length of the drive way required to accommodate all the arrivals, on the average, if 20 feet of

driveway is required for each car that is waiting for the service

Reference books:-

a) MECHANICAL SYSTEM DESIGNK.U.Siddiqui & Manoj Kumar Singhb) MECHANICAL SYSTEM DESIGNALOK GUPTA

Signature of the faculty_________ Signature of the HOD__________