Madurai Kamraj University (MKU) 2006-2nd Year M.C.A Computer Aplications All subject s - Question Paper

M.C.A 2nd Year May 2006


PAPER-I OPTIMIZATION TECHNIQUES

Time: 3 hours maximum: 100marks

PART A ans all ques. (8x5=40 marks)

1. (a) discuss how will you formulate a mathematical model to a provided linear programming
problem. Or (b) Use graphical method to solve the subsequent Max z=3x1 +4X2
Subject to 5X1 + 4X2 <= 200 3x1 + 5X2 <=150 5x1 + 4X2 >= 100 SX1 + 4X2>=8O X1X2
>=O.

2. (a) discuss the various categories of stochastic processes with simple examples. Or (b)
discuss the recurrent class of Markov chain and state the criteria for recurrence.

3. (a) discuss the main characteristics of the Queuing system. Or (b) establish the
probability distribution formula for pure-death process.

4. (a) What is queuing theory? discuss the basic elements of queues. Or (b) At a public
telephone booth in a post office arrivals are considered to Poisson with an avg.
inter-arrival time of 12 minutes. The length of the phone. Call may be presumed to be
distributed exponentially with an avg. of four minutes. compute the following: (i)
What is the probability that a fresh arrival will not have to wait for phone? (ii) What is
the probability that an arrival will have to wait more than 10 minutes before the phone
is free?

5. (a) provide a brief outline of the revised simplex method. Or (b) Write down the dual of
the subsequent LPP Min z = 4x1 + 3X2 -2x3 Subject to 3X1 + 6X2 + 4x3 >=6 seven X1 + X2 +
2x3 >= 5. 6x1 - 2X2 – X3<= nine 2x1 - X2 + 3x3 >= four 4x1 + 6X2 – X3 >= two X1, X2,
X3>=0.

6. (a) discuss a few of the practical applications of Integer programming issue. Or
(b) discuss how the assignment issue can be treated as a particular case of
transportation issue.


7. (a) elaborate the unbalanced assignment problem? How are they solved? Or(b) discuss
the nature of a travelling salesman issue and provide its mathematical formulation.


8. (a) discuss the mechanism of queuing process by considering a few illustration.Or (b) A
customer owning a Maruti car right now has got the choice to switch over to Maruti,
Ambassador or Fiat next time with the probability (0.20, 0.5 and 0.30) provided the
transition matrix.
0040 0.30 0.30
P = 0.20 10.50 0.30
0.25 0.25 0.50 obtain the probabilities with his 4th purchase?


PART B ans ALL ques.. (5 x 12 = 60 marks)


9. (a) Solve the subsequent LPP using simplex method Maximize z =3X1 + 5X2 + 4X3 . Subject
to 2X1 +3X2<=8 2X2 + 5x3 <=10 3x1 + 2X2 + 4X3 <=15 and Xl. X2 X3 >= 0 Or (b) Use revised

Earning:   Approval pending.