# Guru Jambheshwar University 2006 M.Sc Computer Science Computer Based Optimization Methods - Question Paper

(Third/Fourth Semester)

COMPUTER SCIENCE MS-19

Computer Based Optimisation Methods

Time : 3 Hours Maximum Marks : 100

Note : Attempt any Five questions. All questions carry equal marks.

1. Solve the following LPP by using Simplex method and also draw the flow chart of it : Max. Z = 7jcj + Sx_{2}

Subject to ~ *1 2*2 ~ 6 4x_{{} + 3.r_{2} < 12 and x_{i} 0 where * *= 1, 2.

2. (a) Define O.R. and also discuss its

characteristics and limitations.

(b) What do you mean by LPP ? Discuss its applications and limitations.

3. (a) Find the dual of the following Primal

problem :

Min. Z = 2x_{2} + 5*3

Subject to Xj + *_{2} 2 2*j + x_{2} ^{+} 6x3 < 6

^{x}\ ~ ^{x}i ^{+} 3*3 - 4

and jcj, *_{2}, *3

(b) Solve the following problem by using Dual Simplex Method :

Min Z = 3xj + x_{2}

Subject to Xj + x_{2} > 1 2*i + 3*2 2 and *!, *2 -

4. State the necessities of integer programming and solve the following LPP :

Max Z = 7*| + 9*2

Subject to - *j + 3*2 < 6 7*j + *2 < 35 *j, *2 0 and are integers.

5. (a) Discuss the basic steps in PERT/CPM techniques and also discuss its applications.

(b) Consider the following network and find out the time it will take to complete this project :

6. (a) Discuss the following discipline :

(i) FIFO

(ii) CIFO

(iii) SIRO

(b) A car repairman finds that the time spent on his jobs has an exponential distribution with mean 30 minutes. If he repairs car in order in which they come in and if the arrival of cars are approximately Poisson with an arrival rate of 10 per 8-hour day, what is repairman's expected idle time each day ? How many jobs are ahead of the average can just brought in ?

7. Define Markov Process and Markov Chain. Find if the following transitions matrix is regular and ergodic :

1 |
2 |
3 |
4 | |

1 |
0 |
X |
X |
0 |

2 |
X |
0 |
0 |
X |

3 |
X |
0 |
0 |
X |

4 |
0 |
X |
X |
0 |

8. Write short notes on any two of the following :

(a) Customer's Behaviour

(b) Standard form of LPP

(c) Integer Programming

(d) Floats.

J-4262 4 J.300

Attachment: |

Earning: Approval pending. |