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10ME74

Seventh Semester B.E. Degree Examination, Dec.2015 lJan.20l6

Operations Research

hrs.

Max. Marks:,lffi

c, €o !O

€ x1-x2)l;

b. c.

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usinge the graphical method, answer the following questions: Q --r------What are the extreme points for the feasible region? If the problem has an objective function, maximize z' point? iii) If the problem has an objective function, minimize z

D ii)

:

3xr -r xz , what is the optimal

:

point.

3x1

Subjecttoconstraints:2xr +W<6 ; Xr-Xz>3 List any four characteristics of a good model.

lr str Solve the following LPP UV E& ivl method. ; € 2 a. Maximize Z:3booox, {Zpdoo*, *iA r*uw

x2 t what is the optimal (10 Marks) 2x1 + 3x2 (06Marks) (04 Marks)

w

AS

t

Z: ; xr ,xz)O

Solve the following problem using graphical method maximize

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SE E = =ia "*,, troo :E R H; i H ;E AA

*

The following are the two constraints for the LPP under consideration:

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E L a. g E R b0:

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g.

PART-A

6 d

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Note: 7. Answer any FIWfull questions, selecting atleast TWO questions from each part. n (Ise of Normal distribution 2. tables is permitted.

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Time: 3

rB-

E

S

; 5 bE

b.

xz36;

x2>2; Q

xr1_2xz<18;

2x1 + and X1 , x2 ) Write the dual for the iollowing primal. Minimize z;xiffinxr + 35000x2 Subject to*:-,f0xr + 60>t-:2500; 80xr + 60xz > 3000 Non-neg*ffiiy constraints Xr , xz )

*,5M

ed

fi: E&

Subjectto: x2(x1 +.3*W

:

*"o.\ \"qp/i

.p

F5 EE ts E

ia

';

0

(14 Marks)

;

100xr

+

20Oxz> 7000 (06 Marks)

3 a. aAffit is produced by four factories A, B, C & D. The unit production costs in them are EE *W, {1:and {5 respectively. Their production capacities are: Factory A : 50 units ; B : 70 ii ; C 30 units and D : 50 units. These factories supply the product to four stores, the ,*ffiits u ;0 S n demand ofwhichare25,35, 105 and,20 units respectively. Unit transportation cost in rupees 'E q a*1

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from each factory to each store is given in the table below. Stores

Factories

| 23

4

2

t1

4

6

^fr-ail BIl0 10 lalzlsl 7 J 9 t2 c fBTiTtffi Dl4l6l8l3 4 6 J 8

L

13

I

5

I

I

8

I

|

Determine the extent of deliveries from each of the factories to each of the stores so that the total production and transportation cost is (12 Marks)

minimum. I of3

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b.

Four machines Mr , M2 , M: and lVIa are to be installed in a machine shop. There are five vacant places A, B, C, D and E. Owing to the limitations machine Mz cannot be placed at C and M3 cannot be placed at A. The assignment cost of machine i to place j in rupees (1000)

&"

is shown below.

m

A

* \r/S **/ ,a * dm*/

D

4

6

Mz

7

M3

4 6

M4

9

J

5

6

5

4

9

6

2

7

2

J

10

.?r

,B tuq

6

co

Mr

1

d^

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Find the optimal assignment schedule.

(08 Marks)

g.

dt\d

*){-, tg-

Solve the below given integer programming problem: Maximize Z: 4xr * 6x21- 2x3 4xt - 4xz < 5 Subject to

-xt * 6xz<5

xl , x2, x: ) 0 and

X1 , X3 are

!

integers.

S.$

-" 'ilihr

ib

-xt*xzfx:<5

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klJf

$1 .!.__

;*

(20 Marks)

a

-"#

PART,-*#q*

B

Immediate

QFt{mistic Predecessor- %!neb (Hrs) 4

A A A B,C B,C E.F E,F D,H G, I

ia

C

ik

A

w

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Following data rerer fer Io a Activity

D

Time(Hrs) 6

1

4.5

J 4

J

a

Time (Hrs) 8 5

J

5

6

1

1.5

J

4

5

I

1.5

5

0.5

ed

E F G

Most likely Pessimistic

5

6

7

2

5

8

2.5

2.75

4.5

K

J

5

7

H

I

.p

J

Draw the network diagram Find out the ES, EF, LS, LF and slack for each activity. Find out the variance and standard deviation for the critical path. Determine the probability of completing the project in 24 hrs.

a.

Mention and discuss seven elements of a queing system. (07 Marks) Defne : (i) Balking (ii) Renegging (iii) Jockeying (03 Marks) On an average 96 patients per 24 - hours day require the service of an emergency clinic. On an average a patient requires 10 minutes of active attention. The facility can handle only one emergency at a time. Suppose that il costs the clinic {100 per patient treated to obtain an averaging service time of 10 minutes and that each minute of decrease in this average time would cost the clinic 110 per patient treated. How much would have to be budgeted by the

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a. b. c. d.

(20 Marks)

sr..lr*,

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r. 1r-

c.

clinic to decrease the average queue size from

1l patient, ,o I patient? 3' 2'

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(10 Marks)

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A's Strategy

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(04 Marks)

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b.

What are the characteristics of games? Solve the following game by the dominance rule. B's stra b: 1

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7

3

-6

2

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10ME74

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-2

(08 Marks)

You are given the following data regarding the processing times of some jobs on three

ib

8 a.

-7 4

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5 6

g.

Can we formulate the above game as LPP and solve it by simplex / Big-M method? If yes, discuss how? (08 Marks) Solve the following game using graphical approach: B's Strategy br bz b: bq A's Strategy ar8 9

w

ik

machines I, II and III. The order of processingris I - II - III. Determine the sequence that minimizes the total elapsed time required tg"complete all the jobs. Mention clearly the total elapsed time and the idle time of machine Il'aad III. Processi rme (Hours Job Machine I II ru

A'q H""-

J

3

7

2

5

4

5

11

E

9

I

5

F

8

4

6

G

7

J

t2

ia

8

7

.6

ed .,

f**:, Udi

. ,.;\l

*"'

6

,i:rqe 5- D

SA

r q.3

4

(10 Marks)

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is the supervisor of legal-copy-express, which provides copy services for Los Angcrcs r-os Angeles law raw rrms. firms. Five rlve cuslomers customers submitted suomrfteo tner their oroers orders at tne the beginning Degmnmg oI of and are as follows. Schedule the jobs as per i) EDD rule ii) SPT rule and

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Job 0n order of arrival ) Processins Time (Davs) Due date (Davs hence)

A

B

C

D

E

a J

4

6

2

1

5

6

7

9

2 (10 Marks)

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Operations Research Jan 2016 (2010 Scheme).pdf

Following data fer. a. Draw the ... by simplex / Big-M method? If yes, ... You are given the following data regarding the processing times of some jobs on three.

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