B - T 19 - 9Register Number :Name of the Candidate :

5 2 9 0DIPLOMA EXAMINATION, 2007

( PRODUCTION MANAGEMENT )( PAPER - IV )

140. QUANTITATIVE METHODS INMANAGEMENT

December ] [ Time : 3 HoursMaximum : 100 Marks

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Answer any FIVE questions.All questions carry equal marks.

Use of Statistical Tables permitted.1. Solve the following LP problem using the

simplex method :Maximize z = 3x1 + 2x2 + 5x3Subject to : x1 + 2x2 + x3 430,

3x1 + 2x3 460 x1 + 4x3 420.

and x1, x2, x3 0. (20)

5. A fleet owner finds from his past recordsthat the cost per year of running a vehicles,whose purchase price is Rs. 50,000 is

Thereafter, running cost increases byRs. 2,000, but resale value remains constantat Rs. 2,000, but resale value remains constantat Rs. 2,000. Atauhat age replacement is due ?

(20)6. The following failure rate have been observed

for a certain type of light bulbs.

4

End ofweek

prob. offailure to date

1 2 3 4 5 6 7 8

005 013 025 043 068 088 096 100

Year Resale value(Rs.)Resale cost

(Rs.)1 5,000 30,0002 6,000 15,0003 7,000 7,5004 9,000 3,7505 21,500 2,0006 16,000 2,0007 18,000 2,000

B - T 19 - 10

2. Solve the following transportation problem :

(20)3. Consider a problem of assigning four clerks

to four tasks. The time (hours) required tocomplete the task is given below :

Clerk 2 cant be assigned to task A andclerk 3 cant be assigned to task B. Find alloptimum assignment schedules. (20)

2 3

Origin Destination SupplyD1 D2 D3 D4O1 1 2 3 4 6O2 4 3 2 0 10O3 0 2 2 1 8

Demand 4 6 8 6

TasksA B C D

1 4 7 5 62 - 8 7 43 3 - 5 34 6 6 4 2

Clerks

4. Five jobs are performed, first on Machine - Xand then on Machine - Y. The time taken inhours by each job an each machine is givenbelow :

Determine the optimum sequence of Jobsthat minimizes the elapsed time to completethe jobs. Also, complete the minimum time.

(20)

A B C D E12 4 20 14 22

6 14 16 18 10

Tim onMachine - X

Tim onMachine - Y

Job

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B - T 19 - 11

The cost of replacing are individual bulbin Rs. 225, the decision is made to replaceall bulbs simultaneity at fixed intervals andalso, to replace individual bulbs as they fail inservice. If the cost of group replacement is60 paise per bulb and total number of bulbsis 1,000, what is the best interval betweengroup replacement ? (20)

7. (a) Define the following :(i) Activity.(ii) Event.(iii) Critical path.(iv) Optimistic duration.(v) Crash duration.

(b) Draw the network, given the followingprecedence relationship : (10)

5 6

Event numbers : 1 2, 3 4 5 6 7Preceded by : - 1 2, 3 3 4, 5 5, 6

8.The

time a

nd co

st estim

ates a

nd pre

cedenc

e rela

tionshi

p of th

e diffe

rent a

ctivitie

scon

stitutin

g a pr

oject

are gi

ven be

low :

It the

dead

line

of 1

7 we

eks is

impos

ed fo

r com

pletio

n of

proje

ct, wh

atact

ivities

will

be cra

shed ?

(20)

AB

CD

EF

GH

I -

-B

BA

AF

C,F,G

F

38

65

134

26

2 2

64

210

41

41

8,000

60010,

0004,0

003,0

0015,

0001,2

003,5

007,0

0019,

0001,0

0012,

00010,

0009,0

0015,

0001,4

004,5

008,0

00

Predec

essor

activit

y

Activi

ty

Time (

weeks

)( N

ormal)

Cost (

Rs.)

( Norm

al)

( Cras

h )

( Cras

h )

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B - T 19 - 12

9. In a reservation center with a single server,customer aims with the inter arrival time ofthe exponential distributions with mean 10minutes. The service tine is also assumed tobe exponential with mean 8 minutes. Find

(a) Idle time.(b) Average length of queue.(c) Expected time of customers.

10. Briefly explain the following :(a) Monte Carlo simulation.(b) Application of inventory models with the

usage of Dynamic programming. (20)

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