MB 301 - Applied Operation Research (2124) Dec
2004
Note: Section A is
compulsory. Attempt any four Questions from section B.
Section A (2 marks each)
Question 1 :
a.
Give
the Mathematical and Economic structure of the linear
programming problem.
b.
What is the
significance of unbounded solution?
c.
Explain Resources float in the context for project
management
d.
Explain Primal Dual Relationship.
e.
What is
Degeneracy in Transportation problem?
f.
Show that
dual of a dual linear programming problem is the primal
problem.
g.
What is the
difference between free float and total float?
h.
List five
differences between PERT and CPM.
i
Distinguish between Stage and State variable with
reference to dynamic programming.
j.
Explain Saddle point with example.
Section B (10 marks each)
2
Minimize:
Z= -4x+3y
Subject to: x-2y
≥ -4
2x + 3y ≥13
x-y≥4
x , y ≥0
3
Determine optimal solution to the problem given below:
To market
M1
M2
M3
M4
Supply
P1
6
4
9
1
40
From
P2
20
6
11
3
40
Plant
P3
7
1
0
14
50
P4
7
1
12
6
90
Demand
90
30
50
30
4
The
following activities are related to a given
project:
Activity
Time
1-2
8
1--3
6
1-4
4
1-8
4
3-5
7
3-6
2
4-6
6
5-7
5
6-7
9
7-8
5
A
certain type of crane is needed in carrying out activity
2-8, 3-6, 4-6, 5-7. only one crane of this type is
available.
Do
you think the project completion would be delayed due to
this? if yes, by how much.
5
Reduce the following two-sum game to 2x2 order, and
obtain the optimal strategies for each player and the
value of the game:
Player B
B1
B2
B3
B4
A1
3
2
4
0
Player
A2
3
4
2
4
A3
4
2
4
0
A4
0
4
0
8
6
A co At a petrol pump, vehicles arrive at a mean rate of 25
per hour. A vehicle, on an average takes 2 minutes in
taking the petrol. The arrival rates are assumed to
follow Poisson and Exponential distribution,
respectively and there is only one for providing the
petrol. Find out the mean time a vehicle will have to
wait in the queue for getting the petrol.
What other information you can obtain by analyzing the
above queuing system?
7
A manufacturer
purchases an important component at the rate of Rs.42
per piece from a vendor. The requirement of this
component is 1800 per year. If the cost of placing an
order is Rs. 16 and inventory carrying charges per rupee
per year is 20 paisa what should be the order quantity
per order?
