lr- t_

Total No. of Questions-lO1 lTotal No. of Printed Fages-7 f

MBA-II/5

21orrc

M B A cCIuRSE NO. 203

(Management Science)

Time Allowed: 3 Hours Maximum Marks: 70

Note: Attempt five questions selecting one from each {Jnit.

AII questions carrY equal mnrks.

UMT-Il. For the game having the following payoff tabie, use the

graphical procedure to determine the value of the game and

optimal mixed strategy for each player.

strateev

Flayer 2

123

Player 1

I

2

J

4

I -1 3

041? -? {

-3 6-2

2. What is maximin - rninimax principle? Analyze the process

of determination of saddle point for a game.

{Tum Over

rI

I

*'!il!:qrT(2)

UNIT * II

The ABC fast-food restaurant operates a single * channel

service facility for its cusromers. A single ABC employee

takes a customer's order, determines the total cost of the

order, takes the money from the customer, and then fills the

order. Once a customer's order is filled, the employee takes

the order from the next customer waiting for service. The

Poisson probability disuibution describes rhe cusromer

arrivalS. The mean arrival rate is 0.75 customers per minute.

The exponential probability distriburion describes the service

times. The mean service rate is one flrstorler per minute_ For

economic considerations, A"BC evalunes cuslorner waiting

time at $10 per hour qfrile the sewice channel can be ''t

operated for $7 per hcur-

Management is iuterested in developing a better

understanding. of the operatiag characteristics of the food -service waiting line- Specifically, rnanagement worrld like to

know the probability that no customers are in the system, the

average number of customers waiting for sewice, the average

time a customer waits . for service, the probability that an

arriving customer has to wait, and the hourly cost of the

service operation.

I+.

(r)

lYrite a detail note on the application of queuing theory and

general structure of queuing system. Distinguish between

single and multiple channel waiting lines theory model (8'6)

UNTT _ M

5. A manufacfilrer of jeans is interested in developing an

advertising campaign that will reach four different age

groups. Advertising campaigns can be conducted through

TV, Radio and Magazines. The following table gives the

estimated cost in paise per exposure for each age group

according to the medium employed- In addition, maximum

exposure levels possible in each of the media, namely TV,

Radio, and Magazines are 40, 30,20 mittions respectively'

Also the minimum desired exposures within each age group,

namely 13-18, Ig-25,V6-35,36 and older are 3A,25,15 and

10 millions. The objective is to minimize the cost of attaining

the mininlrm exposure level in eaeh age group. Formulate

the above as transportation problem, and find the optimal

solution.

fTurn Over

6.

Media Age Groups

13-18 19-25 26-35 36 and above

TV t2 7 10 10

Radio l0 9 12 10

Magazines L4 12 9 1Z

Five swimmen are eligible to compete in a relay team which

is to consist of four swimmers swimming 4 different

sr,l'immilrg styles; back stroke, brcast sftoke, free style and

butterfly- Jfos firrE taken for the fwe swirers - Rahul,

Kunal, Sadeep, Deqak d Rdit - b otwer a distance of

100m in various sfyks are gim ltfu in sords' Suggest,

which swimtner should k asigd s rtich swimming

style? Who out of five will not be in.ibf relay? Ignre the

state of affairs if somebody is not participating in arry of the

swimming stYle.

Swimmers'€tYles Back stroke Breast Stoke Free stylt Butterfly

Rahul

Kunal

SandeeP

Deepak

Rophit

69

t:80

75

76

80

76

6i65

6

80

12

7t

70

(5)

UNIT _ iV

7. Innis Investments manages funds forand wearthy crienb. The invesrmel

a number of companies

each o&er crient,s needs. ,o, u o.rtt

strategy is tairored to

aurhorized ,o inu.J;,*l^':: : * client, rnnis has been

*m,*;*..,d,ilT?#f{-",:#fi 'Jof r0%; each unit of the money ,n*rr*o

annuar rate of return

provides an annuai rafe of rctu* o, o

ttt fund cost $100 and

minimize nr* ,*,.", ; -::* or 4 %' The client wants to

income from rhe ,::::-- the requirement that the annuai

to Innis's nr* *ottstmenf be at least $ 60'000' According

rsurement system, each unit invested in thestock fund has a risk index of g' and each unif invested in themoney market fund has a risk iadex ,

index associated ri.irh the stock *no ,uot

3; rhe higher risk

is the riskier jnvest

Ieast g 300000 or r"* Innis's

'""nt l'**l u;ttff;:l'Jvested in the money market fund.

(a) Derermine how many units of each fund Innis shouldpurchase for the client to minimize total risk index forthe porrfoiio.

8.

(6)

(b) How much annual income will this invesment strategy

generate?

Use Simplex Method to solve the followrng L'P'P':

9.

Minimize:

Subject to

'When it is difEcult

solving tectrnique for

simulation'' Discuss'

Z=5x+13Y2x +4Y 112

2x +2Y :10

5x +2Y210 x'Y>0

TINIT-V

ts use an optimization technique for

solving a problem one has to resort to

10. (a)

(b)

Explainbriefly CPM and analyzeits applicauon'

Listed in the tabie are the activitiJs and sequencing

necessary for a maintenance job on the heat exchange

in a refinery' Draw a network diagram of activities for

the Project'

A

B

Disrnantle pipe conaection

ilffi'f*:ater'crosureRemove tube bundjet-tean bolts

Clean heater and flcatingheat front

Clean tube bundle

Clean shell

Rephce fube bundle

Prepare shell pressure test

llif* Tube pressure fesrand reassemble

BB

B

CD

E

F

G

H

I

J

C

C

F,G

D,E,H

(6,8)***8********