2266/I/01
1204
ANDHRA UNIVERSITY M.C.A. DEGREE EXAMINATION
FIRST YEAR - SECOND SEMESTER
OPERATIONS RESEARCH

(Effective from the admitted batch of 2000-2001)

Time 3 hours
Max. Marks 75

First question is compulsory.
Answer any FOUR from the Remaining.
All questions carry equal marks.
Write all parts of any question at one place.

1. a. Write a Linear Programming Problem which could have an unbounded solution space using graphical method.

b. Show that the dual of the dual is primal.

c. Explain the method of taking decisions under risk.

d. Explain the importance of moving average technique.

e. State the advantages of simulation.

2. a. A manufacturer of furniture makes two products Chairs and tables. Processing of these, products is done on two machines A and B. A chair requires two hours on machine A and 6 hours on machine B. A table requires 5 hours on machine A and no time on machine B. There are 46 hours of time pet day available on machine A and 24 hours on machine B. Profit gained by the manufacturer from a chair and a table is Rs.25/- and Rs.40/- respectively. Formulate the above as a L. P. P. (7 marks)

b) Using Big M method to Minimize z = 4x₁ + 3x₂ (8 marks)

Subject to the constraints:

2x + x ≥ 10 -3x₁ + 2x₂ ≤ 6 x₁ + x₂ ≥ 6 x₁ ≥ 0 x₂ ≥ 0

3. a. What is the essential difference between regular simplex method and dual simplex method. (6 marks)

b. Use dual simplex method to solve the following L.P.P. (9 marks)

Maximize z = -3x1 - x2
Subject to x1 x  + x2 ≥ 1
2x1 + 3x2 ≥ 2
X1 ≥ 0
X2 ≥ 0

4. a. Formulate the Transportation problem as a Linear Programming Problem. (7 marks)

b. An Airlines company that operate seven days a week has time table shown below. Crews must have a minimum layover of 6 hours between flights. Obtain the pairing of flights that minimizes layover time away from home. For any given pairing the crew will be based at the city that results k a smaller layover:

Flight		Delhi		Calcutta
Number	Depart		Arrive
1		7.00 A.M.	9.00 A.M.
2		9.00A.M.	11.00 A.M.
3		1.30 P.M.	3.30 P.M.
4		7.30 P.M.	9.30 P.M.

Flight		Calcutta	Delhi
Number	Depart 	Arrive
101 		9.00 A.M.	11.00 A.M.
102		11.00 A.M. 	12.00 Noon
103		3.30 P.M. 	5.30 P.M.
104		8.00 P.M. 	10.00 P.M.

For each pair also mention the town where the crew should be based.

5. Solve the travelling salesman problem given by the following data: (15 marks)

C₁₂=20, C₁₃=4, C₁₄=10 C₂₃=5, C₃₄=6, C₂₅=10, C₃₅=10, C₃₅=6, C₄₅=20 where C_ij=C_ji and there is no route between cities i and j if a value for C_ij is not shown.

6. a. Discuss Floyd's algorithm for finding the shortest route.

b. Four factories are engaged in the production of four types of toys. The following of table lists the toys that can be produced by each factory. (9 marks)

Factory 	Toys production mix
1		1, 2, 3
2		2,3
3	 	1,4
4		3, 4

All toys require the same per unit labor and material. The daily capacities of the four factories are 250, 180, 300 and 100 toys respectively. The daily demands for the four toys are 200, 150, 350 and 100 units respectively. Determine the factories production schedules that will most satisfy the demands for the four types.

7. Solve the following Integer Programming Problem by using, branch and bound method: (15 marks)

Minimize z = 4x₁ + 3x₂

Subject to the constraints
5x₁ + 3x₂ ≥ 30
x₁ ≥ 4
x2 ≤ 6
x1₁ ≥ 0
x₂ ≥ 0
and are integers.

8a. Explain simulation. What are its advantages. (6 marks0

b. The following data pertain to the resistance (ohms) and the failure time (minutes) of certain overloaded resistors: (1 + 2+ 6 marks)

Resistance	Failure Time
43		32
29		20
44		45
33		35
33		22
47		46
34		28
31		26
48		37
34	33
46		47
37		30

i. Identify the independent and dependent variables. ii. Draw the scatter diagram.
iii. Fit a curve of the appropriate type.