Enrollment No: _______________________

Exam Seat No:_______________________

C.U.SHAH UNIVERSITY Winter Examination-2015 Subject Name: OPERATION RESEARCH Subject Code: 5CS04ORT1 Semester :IV

Branch:MCA

Date :18/11/2015Time :_2:30_To__5:30__ Marks :70

Instructions: (1) Use of Programmable calculator and any other electronic instrument is prohibited. (2) Instructions written on main answer book are strictly to be obeyed. (3) Draw neat diagrams and figures (if necessary) at right places. (4) Assume suitable data if needed.

SECTION – I Q-1

Attempt the Following questions (1 Mark *7=7) (No MCQ Questions) a. b. c. d. e. f. g.

Q-2

What is OR? Write full Form of LPP What is slack variable What is Artificial variable What is Degeneracy in Transportation problem What is Saddle point What is Optimality check? Attempt all questions

1

2

(07)

Solve following LP Problem Using Graphical Meth Max Z=15X1 + 10X2 Subject to 4x1 + 6x2 ≤ 360 3x1 +0x2 ≤ 180 0x1 +5x2 ≤ 200 and x1, x2 ≥0 A company sells two different products A and B, making a profit of Rs 40 and Rs30 per unit, respectively. The production process has total capacity of 30,000 man-hours. It takes three hours to produce a unit of A and one hour to produce a unit of B. The market has been surveyed and company official feel that the maximum number of unit of A that can be sold is 8000 units and that of B is 12000 units. Formulate this problem can be as an LP model to maximize the profit.

OR Page 1 || 5

(14) (7)

(7)

Q-2

Attempt all questions

(14) (7)

Solve following LP Problem Using Simplex Method Max Z=3X1 + 2X2 Subject to x1 + x2 ≤ 4 x1 - x2 ≤ 2 and x1, x2 ≥0 Write the Algorithm Steps for simplex Method

1

2 Q-3

Attempt all questions

(14) (7)

Apply MODI method and obtain basic feasible solution by VAM

1

I 5 4 4 7

A B C Requirement

II 2 8 6 12

III 4 1 7 17

IV 3 6 5 9

Supply 22 15 8

Find Initial Solution Using NWCM,LCM, & VAM Method

2

(7)

D1

D2

D3

D4

Supply

S1

19

30

50

10

7

S2

70

30

40

60

9

S3

40

8

70

20

18

Demand

5

8

7

14

34

OR Q-3 1

2

Five Men are available to different five jobs find the minimize the total time 2 9 2 7 1 6 8 7 6 1 4 6 5 3 1 4 2 7 3 1 5 3 9 5 1

(7)

Advantage and disadvantages of Linear Programming

(7)

SECTION – II Q-4 a. b. c. d.

Attempt the Following questions (1 Mark *7=7) (No MCQ Questions) What is Feasible Solution? Write the full form of PERT Explain Looping and Dangling What is dummy activity? Page 2 || 5

(07)

e. What is Event? f. What is replacement? g. What is Simulation? Q-5

Attempt all questions 1

2

Given the following pay-off matrix of a two-person zero-sum game, determine the optimal strategies for the players and the value of the game. Is the game strictly determinable? Is it fair? Players A strategies

B1

B2

B3

B4

A1 A2 A3 A4

2 6 -3 2

-2 1 2 -3

4 12 0 7

1 3 6 1

(14) (7)

Players B strategies

Discuss Types of Failure in Replacement Model

OR Q-5 1

2

A dentist Schedule all his patients to 30minutes some patients takes more time and its probabilities given below Category of Times Probability services required (Minutes) Filing 45 0.40 Crown 60 0.15 Cleaning 15 0.15 Extraction 45 0.10 Checkup 15 0.20 Random numbers 40 82 11 34 25 66 17 79 find the average waiting

five jobs each of which must be processed on the two machine A & B Processing time in hours are given Job Machine A Machine B

1 5 2

2 1 6

3 9 7

4 3 8

Determine the sequence of five jobs and total elapsed time.

Page 3 || 5

5 10 4

(7)

Q-6

Attempt all questions 1

(14) (7)

A Research and development department break up is as follows

Job

2

Immediate Time Job Immediate Time Predecessor (Days) Predecessor (Days) A --5 F D 2 B A 7 G C 1 C B 2 H E,F 3 D B 3 I G,H 10 E C 1 (1) Draw the arrow diagram. (2) Identify the critical path and find the total project duration. (3) Calculate total, free and independent floats. The Data collected in running machine is Rs 60000 are given below Year

Resale value

Cost of Spares

1 2 3 4 5

42000 30000 20400 14400 9650

4000 4270 4880 5700 6800

(7)

Cost of labour 14000 16000 18000 21000 25000

Find an optimal replacement of machine

OR Q-6

Attempt all Questions 1

Following table is given calculate the total estimation time, critical path, total and free float For each non critical activity.

Activity A B C D E F

Duration 6 4 7 2 4 10

Predecessor -A B A D E

Page 4 || 5

Activity G H I J K L M

Duration 2 10 6 13 9 3 5

Predecessor -G J,H -A C,K I,L

(7)

2

A book binder has one printing and binding press for 7 manuscripts are as below

Book Printing (Time) Binding (Time)

1 20 25

2 90 60

3 80 75

4 20 30

5 120 90

6 15 35

Determine optimal sequence and total time required for bring all books.

Page 5 || 5

7 65 50

(7)