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 B_2. 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.

 

 

 

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