Manonmaniam Sundaranar University (MSU) 2006 B.Sc Mathematics OPERATION RESEARCH - Question Paper

one two three 4

A 10 12 19 11

B five 10 seven 8

C 12 14 13 11

D eight 15 11 9


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

Processing time (in hours)

job: J1 J2 J3 J4 J5 J6

M1: one three eight five six 3
M2: five six three two two 10

B. using graph method determins the minimum elapsed time sequence of two jobs four machines.

Machines

Job1 Sequence A B C D
Time two four five 1

Job2 Sequence D B A C
Time six four two 3

part 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. obtain the optimum integer solution to Maximize Z=x1+x2 subject to 3x1+2x2<5 x2<2 x1,x2>0

18 a.solve the subsequent assignment issue


A B C D E

I three eight two 10 3
II eight seven two nine 7
III six four two seven 5
IV eight four two three 5
V nine 10 six nine 10

B. obtain 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 subsequent sequence issue

Job

one two three four five 6

M1: eight 10 six seven 11 3
M2: five six two three four 4
M3: four nine eight six five 5

B. using grapical method determins the minimum elapsed time sequence of two jobs five machines.

Machines

Job1 Sequence A B C D E
Time three four two six 2

Job2 Sequence B C A B E
Time five four three two six

Earning:   Approval pending.