Tamil Nadu Open University (TNOU) 2009-2nd Year M.Sc Mathematics Tamilnadu open university Maths Operation research - Question Paper
M.Sc. DEGREE exam –
JUNE 2009.
(AY 2005-06 and CY 2006 batches only)
Second Year
Mathematics
OPERATIONS RESEARCH
Time : three hours Maximum marks : 75
part A — (5 x five = 25 marks)
ans any 5 of the subsequent.
1.Explain the standard form for linear programming issue. Write the standard form of the subsequent.
Maximize
subject to the constraints
2.Explain the basic idea of the interior point used in Karmakar algorithm.
3.What is meant by the term critical activities and why is it necessary to know about them?
4.Obtain the functional formula for maximizing subject to the constraintsand .
5.For the game with the subsequent pay-off matrix, determine the optimum strategies and the value of the game.
6.What do you understand by (a) queue discipline (b) queue size?
7.Define Hessian matrix. Write the sufficient condition for a stationary point , to be an extremum.
8.Show that the issue is separable.
part B — (5 x 10 = 50 marks)
ans any 5 ques..
9.Use simplex method to
Maximize
Subject to the constraints
10.Carry out 3 iterations of Karmakar's algorithm for the subsequent issue :
Maximize
subject to
11.Determine the shortest-route of the network using Acyclic algorithm.
12.Using dynamic programming techniques solve :
Maximize
subject to the constraints
13. For the subsequent pay-off table transform the zero sum game into an equivalent linear programming issue and solve it by simplex method.
Player Q
Q1 Q2 Q3
P1 9 1 4
Player P P2 0 6 3
P3 5 2 8
14. A television repairman obtains that the time spends on his jobs has an exponential distribution with a mean of 30 minutes. If he repairs sets in the order in which they came in, and if the arrival of sets a Poisson distribution approximately with an avg. of 10 per
8 hour day. (a) What is the repairman's expected idle time every day? (b) obtain the avg. number of televisions waiting for service in the system.
15. Examine the function
for extreme points.
16. Find the mean recurrence time for every state of the subsequent Markov Chain .
——————
M.Sc. DEGREE EXAMINATION
JUNE 2009.
(AY 2005-06 and CY 2006 batches only)
Second Year
Mathematics
OPERATIONS RESEARCH
Time : 3 hours Maximum marks : 75
SECTION A (5 5 = 25 marks)
Answer any FIVE of the following.
1. Explain the standard form for linear programming problem. Write the standard form of the following.
Maximize 
subject to the constraints
2. Explain the basic idea of the interior point used in Karmakar algorithm.
3. What is meant by the term critical activities and why is it necessary to know about them?
4. Obtain the functional equation for maximizing
subject to the constraints
and 
.
5. For the game with the following pay-off matrix, determine the optimum strategies and the value of the game.
6. What do you understand by (a) queue discipline (b) queue size?
7.
Define Hessian matrix. Write the sufficient condition for a stationary
point 
, to be an extremum.
8.
Show that the problem 
is
separable.
SECTION B (5 10 = 50 marks)
Answer any FIVE questions.
9. Use simplex method to
Maximize 
Subject to the constraints
10. Carry out three iterations of Karmakar's algorithm for the following problem :
Maximize 
subject to
11. Determine the shortest-route of the network using Acyclic algorithm.
12. Using dynamic programming techniques solve :
Maximize 
subject to the constraints
13. For the following pay-off table transform the zero sum game into an equivalent linear programming problem and solve it by simplex method.
|
|
|
Player Q |
||
|
|
|
Q1 |
Q2 |
Q3 |
|
|
P1 |
9 |
1 |
4 |
|
Player P |
P2 |
0 |
6 |
3 |
|
|
P3 |
5 |
2 |
8 |
14. A
television repairman finds that the time spends on his jobs has an exponential
distribution with a mean of 30 minutes. If he repairs sets in the order in
which they came in, and if the arrival of sets a Poisson distribution
approximately with an average of 10 per
8 hour day. (a) What is the repairman's expected idle time each day? (b)
Find the average number of televisions waiting for service in the system.
15. Examine
the function
for extreme points.
16. Find
the mean recurrence time for each state of the following Markov Chain 
.
| Earning: Approval pending. |
