Deemed University 2010 M.B.A University: Lingayas University Term: III Title of the : Operation Research - Question Paper
Roll No. ..
Lingayas University, Faridabad
MBA, 1st Year (Term III )
Examination May, 2010
Operation Research (BA -109)
[Time: 3 Hours] [Max. Marks: 100]
Before answering the questions, candidate should ensure that they have been supplied the correct and complete question paper. No complaint in this regard will be entertained after examination.
Note: Attempt three questions from Section A and two from Section B. All questions carry equal marks.
Section A
Q-1. Define Operation Research (O.R). What are the advantages & limitation of O.R. Studies?
Q-2. (a) Solve by graphical method
Maxz = -3x + 2y
Subject to
x 3
x y 0
and x, y 0
(b) Solve the following problem by Big M method.
Maxz = x1 + 2x2 + 3x3 x4
Subject to
x1 + 2x2 + 3x3 = 15
2x1 + x2 + 5x3 = 20
x1 + 2x2 + x3 + x4 = 10
and x1 , x2, x3, x4 0
Q-3. Determine the optimum basic feasible solution to the following Transportation problem.
|
|
|
A |
B |
C |
|
|
I |
50 |
30 |
220 |
1 |
|
II |
90 |
45 |
170 |
3 |
|
III |
250 |
200 |
50 |
4 |
|
Required |
4 |
2 |
2 |
|
Q-4. Solve the Assignment problem represented by the following matrix.
|
|
a |
b |
c |
d |
e |
f |
|
A |
9 |
22 |
58 |
11 |
19 |
27 |
|
B |
43 |
78 |
72 |
50 |
63 |
48 |
|
C |
41 |
28 |
91 |
37 |
45 |
33 |
|
D |
74 |
42 |
27 |
49 |
39 |
32 |
|
E |
36 |
11 |
57 |
22 |
25 |
18 |
|
F |
3 |
56 |
53 |
31 |
17 |
28 |
Q-5. For the activity data given below,
Activity to tp tm
(1,2) 2 8 5
to stands for optimistic time tp stands for pessimistic time tm stands for most likely time
(1,3) 1 7 4
(2,3) 0 0 0
(2,4) 2 6 4
(2,6) 5 12 7
(3,4) 3 10 7
(3,5) 3 3 6
(4,5) 2 8 5
(4,6) 4 10 6
(5,6) 2 6 4
(a) Find the probability that the project is completed in 22 days.
(b) Find the probability that the project is completed in 18 days.
Section B
Q-6. (a) Define Game Theory. What are the pure & mixed strategy games.
(b) Solve the following game by graphical method.
|
|
y1 |
y2 |
y3 |
y4 |
|
x1 |
19 |
6 |
7 |
5 |
|
x2 |
7 |
3 |
14 |
6 |
|
x3 |
12 |
8 |
18 |
4 |
|
x4 |
8 |
7 |
13 |
-1 |
Q-7. In a public telephone booth the arrivals are on the average 10 per hour. A call on the average takes 4 minutes. If there is just one phone, find:
(i) Expected numbers of callers in the booth at any time.
(ii) The proportion of the time the booth is expected to be idle?
(iii) Calculate the average time a customer is expected to wait.
(iv) Probability of finding the booth busy.
Q-8. (a) Define standard form of Linear-Programming (LPP).
(b) Define transportation model
(c) Define Queuing -Model
| Earning: Approval pending. |
