OU 2260 OU 2260
Code No. 1082
FACULTY OF MANAGEMENT
MBA II Semester Examination, July August 2016
Subject: Operation 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:
Limitations of O.R.
Goal programming
Unbounded solution
Economic interpretation of dual
Degeneracy in transportation problem
Travelling salesman problem
Assumptions in PERT
Activities in networks
Traffic intensity
Mixed strategy
PART B (5x12 60 Marks)
[Essay Answer Type]
Note: Answer all the questions.
2 Give any five managerial applications of O.R.
OR
Define general linear programming problem. What are its characteristics? Solve the
following L.P. problem graphically:
Maximize z 40x1 30x2
STC 3x1 x2 3000
x1 8000
x2 1200 and
x1, x2 0.
3 Solve the following using simplex method:
Maximize z 3x1 6x2 x3
STC x1 x2 x3 6
x1 5x2 x3 4
x1 5x2 x3 24 and
x1, x2, x3 0
OR
…2.
OU 2260 OU 2260
Code No. 1082

Write the dual of the following L.P. problem and solve it:
Maximize z 3x1 x2 3x3 x4
STC 2x1 x2 3x3 x4 1
x1 x2 x3 x4 3 and
x1, x2, x3, x4 0.
4 Explain traveling salesman problem with a suitable example.
OR
Find an optional solution to the following transportation problem:
Factory
F1
F2
F3
Warehouse W Supply 1 W2 W3
16 20 12 200
160
90
14 8 18
26 24 16
Demand 180 120 150
5 If the indirect cost per day for the project under consideration is Rs. 300 the normal
and crash time and cost estimates for various activities are as given in the following
table. Determine the optimum project duration:
Activity
Normal Crash
Time
(days)
Cost

Time
(days)
Cost

1-2 4 100 3 450
1-3 4 160 2 510
2-4 4 200 4 200
2-3 9 500 4 1,000
3-5 16 2,000 8 2,960
4-5 2 60 1 140
4-6 1 100 1 100
5-7 2 2,500 1 6,000
6-7 4 2,200 3 2,340
6-8 2 700 2 700
7-8 2 2,500 1 6,000
OR
OU 2260 OU 2260
Code No. 1082

5 For the following project, what is the probability of completing in 55 days.
Activity to tm tp
1-2 4 6 8
2-3 5 7 15
2-4 4 8 12
3-6 15 20 25
3-5 10 18 26
4-6 8 9 16
5-7 4 8 12
6-7 1 2 3
7-8 6 7 8
6 A firm has a single channel service station following arrival and service time
probability distributions:
Inter arrival
time (minutes) Probability Service time
(minutes) Probability
10 0.10 5 0.08
15 0.25 10 0.14
20 0.30 15 0.18
25 0.25 20 0.24
30 0.10 25 0.22
30 0.14
The customer's arrival at the service station is a random phenomenon and the time
between the arrivals varies from 10 to 30 minutes. The service time varies from 5
minutes to 30 minutes. The queuing process begins at 10 a.m. and proceeds for
nearly 8 hours. An arrival immediately goes to the service facility if it is free.
Otherwise it waits in a queue. The queue discipline is FIFO. If the attendant's wages
are Rs. 10 per hour and the customer's waiting time costs Rs. 15 per hour, then
would it be an economical propertation to engage a second attendant? Use Monte
Carlo simulation.
OR
Solve the following game:
Player A 3 2
3