Loyola College B.Sc. Statistics April 2008 Operations Research Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

NO 29

 

SIXTH SEMESTER – APRIL 2008

ST 6601 – OPERATIONS RESEARCH

 

 

 

Date : 21/04/2008                Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

 

SECTION – A

Answer ALL questions:                                                                                (10 x 2 = 20)

 

  1. Define basic feasible solution and optimal solution in a linear programming problem.
  2. Rewrite into standard form:
  1. What is the role of artificial variables in linear programming?
  2. Write the dual of :
  1. Explain a transshipment problem
  2. What is an unbalanced transportation problem?
  3. Distinguish between CPM and PERT in network analysis.
  4. Define activity and event in network analysis.
  5. Define decision under uncertainity
  6. Give an example of a 3 x 3 game without a saddle point.

 

SECTION – B

Answer any FIVE  questions.                                                                      (5 x 8 = 40)       

 

  1. The standard weight of special type of brick is 5kg and it contains two basic ingredients B1 and B2. B1 costs Rs. 5/kg and B2 costs Rs. 8/kg. The strength considerations dictate that the brick contains not more than 4 kgs of B1 and a minimum of 2 kgs of B2. Find graphically the minimum cost of the brick satisfying the above conditions.
  2. Show that the following linear programming problem has an unbounded solution.
  1. Explain how you will solve a travelling salesman problem.
  2. Draw the network diagram given the following activities and find the critical path.

Job                               :           A         B         C         D         E          F          G        H        I             J         K

Time (days)     :           13        8          10        9          11        10          8        6         7          14       18

Immediate                   –           A         B         C         B         E          D,F      E         H         G,I         J

Predecessor     :

 

  1. Explain the maximal flow problem.

 

  1. Solve the following problem for the minimum time:
I II III IV V
A 16 13 17 19 20
B 14 12 13 16 17
C 14 11 12 17 18
D 5 5 8 8 11
E 3 3 8 8 10

 

 

 

  1. A decision problem is expressed in the following pay-off table (Rs.’ 000s). What is the maximax and maximin payoff action?

 

Strategy

 

State I II III
A 1880 1840 1800
B 1620 1600 1640
C 1400 1420 1720

 

 

 

 

  1. How will you solve a game problem using linear programming?

 

SECTION – C

Answer any TWO   questions.                                                                      (2 x 20 = 40)

 

  1. a) Discuss in brief duality in linear programming (8)
  2. b) Solve using dual simplex method:

 

  1. a) Explain Vogel’s method of finding an initial solution to a transportation problem.      (8)
  1. b) Use least cost method to find initial basic feasible solution and then find the minimum transportation cost for the following problem.

 

Destinations

D1 D2 D3 D4 Supply
01 1 2 1 4 30
Origins 02 3 3 2 1 50
03 4 2 5 9 20
Demand 20 40 30 10 100
  1. a) Explain  i) total float ii) free float and

iii)independent float in network analysis (8)

 

  1. b) The time estimates in weeks for the activities of a PERT network are given below:

 

Activity: 1-2 1-3 1-4 2-5 3-5 4-6 5-6
Opt.time: 1 1 2 1 2 2 3
Most likely time 1 4 2 1 5 5 6
Pessimistic time: 7 7 8 1 14 8 5
  1. Draw the network diagram and find the critical path
  2. Find the expected length and variance of the critical path.
  • What is the probability that the project is completed in 13 weeks? (12)
  1.  a) Explain Laplace and Hurintz criteria in decision theory
  1. b) Solve the following game graphically.

 

 

 

Go To Main page

 

Latest Govt Job & Exam Updates:

View Full List ...

© Copyright Entrance India - Engineering and Medical Entrance Exams in India | Website Maintained by Firewall Firm - IT Monteur