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Posted Date: 26 Dec 2008      Posted By:: kalaiselvid    Member Level: Silver    Points: 5 (Rs. 1)

2006 Manonmaniam Sundaranar University B.Sc Mathematics OPERATION RESEARCH Question paper



Course: B.Sc Mathematics   University/board: Manonmaniam Sundaranar University





Choose the correct answer. (10X1=10)

1. What is an unbounded solutions?
a. finite number of solutions
b. infinite number of solutions
c. feasible solution
d. infeasible solution.

2. There is a dual constraint for every -------
a. dual variable
b.primal variable
c.primal constraint
d. feasible solution.

3. A basic feasible solutions is optimum if
a.Zj-Cj<0 b. Zj-Cj>0 c. X1,X2,......Xn>0 d. X1,X2,.....<0.

4. Dual simplex method is applicable to the L.P.P having
a. an optimum solution b. an infeasible solution c. an optimum and feasible solution d. an optimum and feasible solution.

5. A transportation problem is said to be balanced if
a. Total supply > Total demand b. Total supply < Total demand c. Total supply = Total demand=0 d.Total supply = Total demand.

6. The current basic feasible solution of the transportation problem is optimal if
a. one Zij-Cij<0 b. all Zij-Cij<0 c. oneZij-Cij>0 d.all Zij-Cij>0

7. In the optimum solution of the assignment problem, a given row or column of the cost matrix have ----
a. no assignment b. <0assignment c.>2 assignment d. one assignment.

8.If Cij > 0 such that minimum Cij =0 then xij provides
a. optimum solution b. feasible solution c. infeasible solution d. unbounded solution.

9. The sequence of jobs and the order of completion of jobs are
a. dependent b. independent c. minimum d. maximum.

10. In graph method the diagonal line segment shows that
a. no job is under process b.first job is under process c. second job is under process d.both jobs are under process

Answer All Questions (5x6=30 marks)

11. a. Write the standard form of the linear programming problem.
b.solve graphically: Max Z=3X1+2x2 subject to 2x1+x2<40 x1+x2<24 2x1+3x2<60 x1+x2>0.

12.a. Use penalty method to solve Max Z=3x1+2x2 subject to 2x1+x2 <2 3x1+4x2>12 x1,x2>0

b. Prove that the dual of the dual us primal.

13. a. Obtain an initial basic feasible solution to the folloeing transportaion problem using the matrix minima method . D1 D2 D3 D4

01 1 2 3 4 6

02 4 3 2 0 8

03 0 2 2 1 10

4 6 8 6

b. Explain Vogels approximation method.

14.a. Write Hungarian assignment algorithm.

b. Solve the following assignment problem:

1 2 3 4

A 10 12 19 11

B 5 10 7 8

C 12 14 13 11

D 8 15 11 9


15.A. determine the sequence for 6 jobs 2 machines that will minimise the total elapsed time T.

Processing time (in hours)

job: J1 J2 J3 J4 J5 J6

M1: 1 3 8 5 6 3
M2: 5 6 3 2 2 10

B. using graph method determins the minimum elapsed time sequence of 2 jobs 4 machines.

Machines

Job1 Sequence A B C D
Time 2 4 5 1

Job2 Sequence D B A C
Time 6 4 2 3

SECTION C (5X12=60 Marks)

16 a. Use Simplex method to Maximize Z= 5x1+4x2
subject to the constraints 4x1+5x2<10 3x1+2x2<9 8x1+3x2<12 x1,x2>0

b. Use simplex method to maximize Z= 107x1+x2+2x3 subject to the constraints 4x1+5x2<10 16x1+x2-6x3<5 3x1-x2-x3<0 x1,x2,x3,x4>0

17 a. usal dual simplex method to solve Minimize Z=3x1+x2 subject to x1+x2>1 2x1+3x2>2 x1,x2>0b. Find the optimum integer solution to Maximize Z=x1+x2 subject to 3x1+2x2<5 x2<2 x1,x2>0

18 a.solve the following assignment problem


A B C D E

I 3 8 2 10 3
II 8 7 2 9 7
III 6 4 2 7 5
IV 8 4 2 3 5
V 9 10 6 9 10

B. find the optimum assignment and the maximum profit for the following:


A B C D E

I 32 38 42 28 40
II 40 24 28 21 36
III 41 27 33 30 37
IV 22 38 41 36 36
V 29 33 40 35 39

20 a.solve the following sequence problem

Job

1 2 3 4 5 6

M1: 8 10 6 7 11 3
M2: 5 6 2 3 4 4
M3: 4 9 8 6 5 5

B. using grapical method determins the minimum elapsed time sequence of 2 jobs 5 machines.

Machines

Job1 Sequence A B C D E
Time 3 4 2 6 2

Job2 Sequence B C A B E
Time 5 4 3 2 6













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