Maharashi Dayanand University (MDU) 2007 M.B.A operational research - exam paper

UNIT I

Que1. Explain the concept of Management Science and its role in Decision Making.

Que2. Solve the Linear Programming issue by Simplex Method :
Max Z = 10 X1+ eight X2 – six X3
Subject to 3 X1 + X2 ? two X3 <= 10
?2 X1 + three X2 ? X3 ? 12
X1, X2, X3 ? 0

Que3. Identify the difference ranging from Integer and Goal Programming. provide example.

Que4. Maximize Z = 30 X + 40 Y
Subject to 60 X + 120 Y ? 12,000
8 X + five Y ? 600
3 X + four Y ? 500
and X ? 0, Y ? 0
by using Simplex Method. Also write its dual.

Que5. Solve the subsequent LPP by using Simplex Method :
Maximize Z = 60 x + 50 y
Subject to 2 x + four y ? 50
3 x + two y ? 60
x, y ? 0.



UNIT II

Que1. Give the main characteristic features of a Transportation issue. How would you determine whether a provided transportation solution is optimal or not ?

Que2. Solve the subsequent Transportation issue for Maximization :
Origin Destination
I II III IV Supply ?
A
B
C 40 25 22 33
44 35 30 30
38 38 28 30 100
30
70
Demand ? 40 20 60 30

Que3. Solve the subsequent Assignment issue to Minimize the total time taken to do all the jobs : what is the total time ?
Operators Jobs
1 two three four 5
A
B
C
D
E
F 6 two five two 6
2 five eight seven 7
7 eight six nine 8
6 two three four 5
9 three eight nine 7
4 seven four six 8


Que4. Using any improper method , solve the subsequent issue to minimize the Total Transportation Cost :
From/To X Y Z Supply
A 6 4 1 50
B 3 8 7 40
C 4 4 2 60
Demand 20 95 35 150

Que5. What is an Assignment issue ? When is an assignment issue regarded as ‘Unbalanced’ ?

Que6. Based on previous experience, time taken by workers on different jobs is provided in the subsequent table (in hours) :
Job
Worker I II III IV
A 45 40 51 67
B 57 42 63 55
C 49 52 48 64
D 41 45 60 55


Determine the Optimal Assignment of the workers to various jobs to minimize the total time.

Que7. Explain :
(a). Transhipment
(b). Traveling Salesman issue.


UNIT III

Que1. For the subsequent project :
Time(days)
Activity Dependence Optimistic Most Likely Pessimistic
A
B
C
D
E
F ?
?
A
B
C,D
B 2
9
5
2
6
8 5
12
14
5
9
17 14
15
17
8
12
20
Draw the network. obtain the Expected Project Completion Time. What is the Probability that the project will be completed in 30 days ?

Que2. A project plan is as follows :
Activity Predecessors Time
A __ 8
B __ 2
C A 1
D B 9
E B 4
F C,D 5
G E 6
H E 3
I G 3
J H 5
K I,J 2
L F 1
Construct a PERT network and complete the Early Start, Late begin and Slack time for every activity. Indicate the Critical Path.

Que3. Write a lucid on Decision-making under uncertainty and risk.


Que4. A newsprint boy has the subsequent probability of selling a magazine :
No. of copies sold : 10 11 12 13 14
Probability : 0.10 0.15 0.20 0.25 0.30
Cost of a copy is Rs. 10 and sale price is Rs. 15. He cannot return unsold copies. How many copies should he order ?

Que5. Explain any 2 of the subsequent :
(a). Pay off table w.r.t. decision under uncertainty
(b). Decision Tree
(c). Expected value of perfect info.

Que6. Write short notes on the subsequent :
(a). Bayesian Analysis
(b). Decision Tree.


UNIT IV

Que1. What is Simulation ? discuss its process, its advantages and limitations ?

Que2. In a railway marshalling yard, goods train arrive at the rate of 30 trains per day. presume that the inter arrival time follows an exponential distribution and the service time is also to be presumed as exponential with mean of 36 minutes. compute :
(i) the probability that the yard is empty.
(ii) The avg. queue length assuming that the line capacity of the yard is nine trains.

Que3. What is game theory ? discuss the principle of dominance and solve the subsequent game :

B1 B2 B3 B4
A1 8 10 9 14
Player A A2 10 11 8 12
A3 13 12 14 13




Que4. Solve the subsequent game for mixed strategy :
B
A B1 B2 B3 B4
A1
A2
A3
A4 25 20 14 30
27 16 12 14
35 eight 15 19
?8 eight 13 0

Que5. Explain :
(a). Assumptions of Game Theory
(b). Saddle point and Principle of Dominance.

Que6. In a hospital 3 doctors who can treat patients equally efficiently. Arrival rate is 6/hour on an avg.. avg. service rate per doctor is Rs. three per hour. obtain :
(a). Average time spend in the system
(b). Average number of idle doctors

Earning:   Approval pending.