2012-Management Science in Decision Making

Total No. of Questions - 101 [Total Nc. cf Pr-intcd pagcs - g

MBA_IIl5

216522

M.B.A.

(Management Science

in Decision Making )

( New Course )Time Allowed: 3 Hours Maximum Marks: 70

l{ote: Attempt Jive questions in ail serecting one question Ji"orneach Unit. Each question cayries 14 marlcs.

TINIT _ Il. A manufacturer makes a product, of'which the principal

ingredient is a chemicar X. At the moment, the manui.acturer

spends Rs.l000 per year on supplv of X, but there is a

possibility that the price may soon increase to four times itspresent figure because of a worrdwide shortage of thechemical. There is another chemical y, which the

manufacturer could use in conjunction with the third chemical

Z in order to give the same effect as chemical X. chemicar y& Z would together cost the manufacturer Rs.3000 per year,

but their prices are unlikely to rise. what action should the

manufacturer take:

(a) Apply the Maximin and Minimax criteria for decision

making and give two sets of solutions.

couRsE NO.203

z.

(2)

(b) If the coefhcient of optimisn is 0'4' find the course of

action that minimizes the cost'

A businessman has trvo independent investment portfolios A

and B available to him, but he lacks the capital to underlake

both of them simultaneously' He can choose A first and then

stop, or if A is not successful' then take B or vice-versa' The

probabiliry of success of A is 0'6' while for B is 0'4' Both the

investment schemes tequire an initial capital outlay of

Rs.10,000 and both return nothing if the venture is

unsuccessfui. Successful completion of z\ u'ill retum

Rs.20,000 (over cost) and successflil completion of B will

retum Rs'24,000 (over cost)' Draw a decision tree and

determine the best strategY'

UNIT - II

3. Using the penalty (Big-M) method solve the following LP

problem:Maximize'Z: xl * 2x2+ 3 x3 - xa

Subject to constraints

x1 + 2 xz+3 x,r = 15

2x1 -x2t5x;=20x1*2Xz*x:*x+:10where X1, X2' x3, Xa Z 0

Ii

(3)

The XYZ company has the option of producing two productsduring period of srack activity. For the next period, productionhas been schedured so that the miting machine is free for r0hours and skilled rabour wiil have g hours of time available.

For the above Lp problem:

(a) Write dowathe dual form

(b) obtain the optimar sorution for the primar form.

UNIT _ IIIA company has three factories (Fr, Fz & F: ) which supply tcthree warehouses ( W1,W2 & W: ). Weekly factory capacitiesare 200' 160 and g0 trnits respectivery. weekry warehouserequirements are 1g0, r20 and 150 units respectivery. The unitshrpprng costs (in rupees) are as given below:

Product Machine timePer unit

Skilled labourfime ner rr.r't

Prnfit contributionpcr unit

5---.--.---.==_-----J,

A 4 2B 2 2

wl w2 w3

Fl

F'2

F3

I6

l426

20

I24

l)

I8

I6

(4)Obtain air

ii) Initial soluticn for the given ffanspoflation problern

' using Vogel's Approxinia:!+n Method: and

(ii) Optimal solutlcn hr the given trailspcftation

probic:n using MODI method.

A small airlines company, owning five planes operaie-q on all

ihe seven days of the week. Flights between ihe three cities A,

B and c a*cording to the schedule is given in the table belor,v.

The layover cosi psr stop is roughly proportional to the sqllare

of the layovcr time.:

FlightNo From I Departure timeI (in hours)

To i Arrival time

| ( in hours)

1

2

J

4

5

6

I

8

9

10

A

A

A

A

A

B

B

B

C

C

09:00

10:00

15:00

20:00

22:00

04:00

11:00

15:00

07:00

15:00

B

B

B(-

C

A

l2:00

13:00

18:00

Midnight

02:00

07:00

14:00

18:00

I 1:00

19:00

A

A

A

A

!

I

I

i

I

I

I

I

7.

(s)

Find how the pian';*s should be assigned to the rlights so as to

rniniinize the tctal la3'over cost? \l.hile solving for the above

problem assurne the foll*wing conditions:

(a) A plane cannot make more than two trips ( to and fro);

(b) A plane flying from a particular destination mirst be back

within 24 hours fcr the next scheduled trip from the

destination.

LINIT - IVThe following is the table showing details of a project:

The indirect cost is Rs.400 per day

(a) Draw the network diagram and identify the critical path;

(b) What are the normal project duration & associated cost;

ActivitlImmediatePredecessor

Normal CrasTime(in davs)

Cost(in Rs,'0001

Time{in davs

-T;st(in Rs.'000i

A

B

C

D

E

F

G

B

B

B

E

A,D,C

t0

8

5

6

8

5

t2

20

1s

8

11

9

5

3

7

6

4

4

5

4

8

30

2A

l4

15

15

8

4

8.

(6)

(c) Crash the relevant activities systematically and determine

the optimum project cornpletion time and cost.

'lhe data for a PERT network is displayed in the table below:

Time Estimates (in days)

Activity Sequence Optimistic Most likely Pessimistic

l-2I -3l-4t- J

2-53-43-64-65-6

(a) Draw the network

Path.

666612242s8

l1 l4

15 24

369 15

410diagram and determine the critical

23

45

9

27

16

(b) What is the expected duration of completion of the entire

project?

(c) What is the probability that the project duration will

exceed 60 days?

(d)

(e)

(7 )

What is the chance of completing the project between 45

days and 54 days?

It becomes known later that the three time estimates for

the activity 4 - 6 have to be revised to 14, 20 and.32 for

Optimistic, Most Likely and Pessimistic time estimates

respectively. What impact does this have on the project

duration? What will be the probability that the project

can now be completed before 46 days? For the above

PERT problem the additional data.given is as fallsws:

z 0.40 4.25 A.50 0.75 1.0A t.S0 I.6T

(zsz) a.s00 0.599 0.692'0.778 0.84r 0.9s3 0.9s3

UNIT _ V

In a small town, there are only two stores, ABC & XyZ, that

handle sundry goods. The total number of customers is equally

divided between the two, because price and quality of goods

sold are equal. Both the stores have good reputation in the

community, and they render equally good customer service.

Assume that a gain of customers by ABC is a loss to XyZ and

vice-versa. Both the stores plan to run annual pre-Deepawali

sales during the first week of November. The sales are

9.

l'6.'

advertised through a local newspaper, radio and television

rnedia. With the aid of the advertising firm, store ABC

consffucted the game matrix as given below (the figures in the

matrix represent a gainor loss customers.

Strategt of ABC Nauspaper Radio Television

Newspaper

Radio

Television

30 40

01590 20 s0

10.

Determine the optimal strategies and the worth of such

strategies for both ABC and XYZ stores. ,

A bakery keeps stock of popular brand of cake. The daily

demand based on past experience is"liven below:

Daily Demand 0 15 25 35 45 50

Probability 0.01 0.15 0.2a 0.50 a.n 0.02

Consider the foliowing sequence of random numbers:

48,78, Ag, 51,56, 77, 15, 14, 68and09.

(a) Using the sequence, simulate the demand for the

next 10 days.

(b) Find the stock situation if the owner of the bakery

decides to make 35 cakes everyday. Also estimate the

daily average demand for the cakes on the basis of the

simulated data.

*******d<{<*****

Strateg,, of XYZ