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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__________