FACULTY OF MANAGEMENT
MBA II Semester Examination, May/June 2017
Subject: Operations Research
Course No. 2.5
Time: 3 Hours Max. Marks: 80
PART A (10x2 20 Marks)
[Short Answer Type]
Note: Answer all the questions.
1. Explain the following briefly.
Characteristics of OR.
Non-linear programming
Linear programming problem
Primal Dual relationship
Travelling salesman problem
Restricted assignment problem
Assumptions in PERT
Total and free floats
Queue discipline
Pay-off matrix
PART B (5x12 60 Marks)
[Essay Answer Type]
Note: Answer all the questions using internal choice.
2 Define Operations Research (O.R). Explain its nature and give the managerial
applications of O.R.
OR
Define general linear programming problem. What are its characteristics? Solve the
following L.P. problem graphically:
Maximize z 7x1 3x2
STC x1 2x2 3
x1 x2 4
x1 5
2
x2 3
2
and
x1, x2 0
3 Given the L.P. problem solve using simplex method.
Maximization z 200x1 150x2 150x3
STC 10x1 3x2 10x3 100
5x1 5x2 5x3 60 and
x1, x2, x3 0
OR
…2.
OU 2260 OU 2260
Code No. 9092

Write the dual of the following L.P problem and solve it.
Maximize z x1 x2 x3
STC x1 3x2 4x3 5
x1 2x2 3
2x1 x3 4 and
x1, x2, x3 0
4 Find an optimal solution to the following transportation problem:
Destination D Supply 1 D2 D3 D4 D5
S1 5 8 6 6 3 8
Source S2 4 7 7 6 5 5
S3 8 4 6 6 4 9
Demand 4 4 5 4 8
OR
Find an optimal solution to the following assignment problem.
Job
Contractor 1234
a b c d
10 24 30 15
16 22 28 12
12 20 32 10
9 26 34 16
5 Determine the maximal flow and the optimum flow in even are for the following
network.
OR
…3.
OU 2260 OU 2260
Code No. 9092

A small project has the following details:
Activity Predecessor Activity time (days)
Optimistic Pessimistic Likely
A 3 11 7
B A 14 28 21
C A 11 17 14
D C 2 2 2
E B 2 8 3.5
F E 10 21 14
G F 3 5 4
H F 4 8 4.5
I H 1 4 2
Draw the network diagram and compute the expected completion time of the project.
ii) Find the total and free float for non-critical activities.
iii) What is the probability that the length of the project does not exceed 56 days?
6 Solve the following game:
Player B
Player A





10 5 2
13 12 13
16 14 10
OR
Observations of past data show the following patterns in respect of inter arrival
durations and service durations in a single channel queuing system. Simulate the
queue behaviour for a period of 60 minutes and estimate the probability of the
service being idle and the mean time by a customer waiting to be served.
Inter arrival time Service time
Minutes Probability Minutes Probability
2 .15 1 0.10
4 0.23 3 0.22
6 0.35 5 0.35
8 0.17 7 0.23
10 0.10 9 0.10
Random numbers (Start at North-West corner and proceed along the row)
97 14 72 10
21 81 87 90
38 10 29 17
11 68 99 51
40 30 52 71