Roll No. ......................

Total No. of Questions : 09]

J ,{

B.Tech. (Sem. - 7th/8th)

OPERATIONS RESEARCH

SUBJECT CODE: ME -406

Paper ID : [AQ840](Note: Please fill subject code and paper ID on OMR)

Time: 03 Hours

Instruction to Candidates:

1) Section -A is Compulsory.

2) Attempt any Four questions from Section -B.3) Attempt any'Two questions from Section - C.

Ql)

, a)

b)

.c)

d)

e)

t)

g)

h)

i)

. j)

Section -A

Define Operation Research?

Name the different mathematical models?

What is linear.programming?

Give ex~mples of Probabilistic models?

)¥hat is a transportation model?

Construct a typical decision tree?

What is dynamic programming?

Whatis queuing system?

Define 'PERT'?

Define Probabilistic demand?

Section -B

Q2)US6 Big 'M'method to maximize

z = 3XI- X2subject to the constraints2x1+X2 ~2Xl + 3X2 ~3.x2~4, Xl' X2~O

J-552[8129]

[Total No. oCPages : 03

. Maximum Marks: 60

(10 x 2 =20)

(4 xj =20)

P. T.O~

Q3) Using Vogel's approximation method to obtain an initial feasible solution ofthe following transport problem.

. D E F G Available

A'

'B

C L-Requkement 200 225 275 250

250

300

400~

. Q4) Solve the minimal assignment problem whose effectiveness matrix is givenbdow:. .

1 3 42

I

II

III

IV

Q5) Find the critical path of.the following project after drawing the complete... network diagram. Also calculate the project completion cost?

J-552 2,

11 13 17 14

16 18 14 1021 24 13 10

2 3 4 5

4 5 6 7-7 8 9 8

3 5 8 4

Activity Timeduration Immediate

(days) Predecessor

A 4 --

B 3 -

C 5 A

D 7 C

E 6 B

F 2 E

G 2 E

H 5 F-I 6 G

J . 4 D, H, I

Q6) A.small.industry finds from the past data that the cqst of making an item isRs. 25, the selling price of the it~m is Rs. 30 if it is sold within a week, and it~d be disposed off at Rs. 20 per item at the end of the week if unsold.Frequency of weekly sales is given below:

Find the optimum number of items per week the industry should make?

Section - C

Q7) (a)

(2 'x 101= 20)

For a game with th~ following payoff matrix, determine the optimalstrategies and value of the game.

B

A[

6 - 3

]-3 0~.

(b) Describe the basic steps in the procedure of simulation by Monte-Carlomethod?

Q8) . Customers arrive at a sales counter manned by a single person according to aPoisson process with a mean rate 0[20 per hour. The time required to serve acustomer has an exponential distribution with a mean of 100 seconds. Findthe average waiting time of a customer?

Q9) Write short note on anv two of the following:

(a) EOQ.

(b) Replacement Policy.

(c) Game Theory;

...;

~

J-552 ,3

Weeklysales <3 4 5 6 7 >8-No. of weeks 0 10 20 40 30 0