The document contains a practice exam for an Operations Research course. It has two sections - Section A with short answer questions and Section B with longer questions involving calculations. Section A covers topics like linear programming, transportation problems, game theory, PERT/CPM. Section B questions involve using the simplex method to solve a linear program, analyzing OR models and properties, solving a transportation problem to minimize distance, and constructing a CPM network for a project with activities. Students must answer one question from each of the four units which cover linear programming, transportation/assignment problems, queuing theory, and project management techniques like CPM/PERT.

1. KEDARNATH AGGARWAL INSTITUTE OF MANAGEMENT
INTERNAL EXAMINATIONS, APRIL 2018, MBA 2nd Sem.
Time:3 Hours Operations Research Max. Marks :80
Note: Section A is compulsory. In section B, attempt one question from each unit.
Section-A
Q.1 What is Saddle point show with the help of an example.
Q.2 What are the assumptions of Linear Programming Problems?
Q.3 Explain four difference between PERT & CPM.
Q.4 What do you mean by duality in LP, illustrate?
Q.5 explain dominance rule of row and column in game theory?
Q.6 What is unbalanced transportation problem, illustrate?
Q.7 What is dummy activity, explain & illustrate?
Q.8 What is balanced transportation problem?
Section-B
UNIT-1
Q.1 Solve the following LP problem using simplex method:-
Maximize Z= 6X1 + 8X2
Subject to 5X1 + 8X2 < 60
4X1 + 4X2 < 40
X1 & X2 > 0
Q.2 (A)Discuss in detail the essential characteristics & different models of OR.
(B)Describe properties of linear programming in detail?
UNIT-2
Q.3 A company is producing a single product and is selling it through five agencies situated
in different cities. All of a sudden, there is a demand for the product in another five cities not
having any agency of the company. The company is faced with the problem of deciding on
how to assign the existing agencies to dispatch the product to needy cities in such a way that
the travelling distance is minimized. The distances (in kms.)between the surplus and deficit
cities are given in the following distance matrix:- (here DC- deficit cities & SC- surplus
ciyies)

2. DC
SC
I II III IV V
A 160 130 175 190 200
B 135 120 130 160 175
C 140 110 155 170 185
D 50 50 80 80 110
E 55 35 70 80 105
Determined the optimal assignment schedules.
Q.4 A co. has three production facilities S1, S2, & S3 with production capacity of 7, 9 and 18
units (in 100s) per week of a product, respectively. These units are to be shipped to four
warehouses D1, D2, D3 & D4 with requirement of 5, 6, 7 and 14 units (in 100s) per week,
respectively. The transportation costs (in rupees) per unit between factories to warehouses are
given as follows:
Warehouses
Determine the initial solution (by VAM Method) optimal distribution for this co. in order to
minimize its total transportation cost.
UNIT-3
Q.5 list out and explain terminology used in queuing system and also describe application
areas of queuing theory.
Q.6 from the payoff matrix solve its optimally
3 2 4 0
3 4 2 4
4 2 4 1
3 4 3 4
UNIT-4
7. Consider table given below, summarizing the details of a project involving 14 activities.
Project Details
Activity Immediate predecessor(s) Duration (months)
A - 2
B - 6
C - 4
D B 3
E A 6
D1 D2 D3 D4 Supply
S1 19 30 50 10 7
S2 70 30 40 60 9
S3 40 8 70 20 18
Demand 5 8 7 14
Player B
Player A

3. F A 8
G B 3
H C,D 7
I C,D 2
J E 5
K F,G,H 4
L F,G,H 3
M I 13
N J,K 7
a) Construct the CPM network.
b) Determine the critical path and project completion time
c) Compute total floats and free floats for non-critical activities.
Q.8 write short note on:-
(i) Difference between PERT & CPM
(ii) Phases of project network
(iii) Crashing of project Network.
(iv) free floats & total floats