Annamalai University 2008-1st Year B.C.A Computer Application " 530 SCIENTIFIC COMPUTING " ( - I ) ( PART - III ) ( ) 6 6 8 0 - Question Paper

4

4. Determine the sequence that minimize the total time required to complete the following poles on three machines :

Job :	1	2	3	4	5	6	7
Machine-I :	4	9	8	5	10	9	8
Machine-II :	5	4	3	6	2	5	4
Machine-Ill :	7	8	6	12	6	7	13

5. (a) Let

A = { 1, 2, 3, 4 }

and R { (1, 1), (1, 4), (2, 1), (2, 2),

(3, 3), (4, 4) }

Use Warshalls algorithm to find the transitive closure of R.

(b) Let

f(x) = x + 3, g(x) = x - 2 and h(x) = 3x,

for x g R, the set of real numbers.

Find gf;fg; ff; gg, fh;hg;hf; and f g h.

Name of the Candidate :

6 6 8 0 B.C.A. DEGREE EXAMINATION, 2008

(FIRST YEAR)

(PART - III)

(PAPER - I)

530. SCIENTIFIC COMPUTING

( New Regulations )

December ]    [ Time : 3 Hours

Maximum : 100 Marks

Answer any FIVE questions.

All questions carry equal marks.

(5 x 20 = 100)

1. (a) Use graphical method to Minimize

z = 6,000 x_: + 4,000 x₂ Subject to

3x_: + x₂ > 40 x_: + 2-5x₂ > 22

3x_: + 3x₂ > 40

   Turn over

x_p x₂ > 0.

(b) Use BIG - M method to solve the following LPP:

Minimize

z = 4x + 3x₂

Subject to

2x + x₂ > 10

-3x₁ + 2x₂ < 6

x_: + x₂ > 6

x_r x₂ > 0.

2. (a) Use dual simplex method to Maximize

z = x₁ + 6x₂ Subject to

Xi + x₂ > 2 x₁ + 3x₂ < 3 x_r x₂ > 0.

(b) Solve the following travelling salesman problem:

A B

From

D

E

F

3. State the computational procedure for the solution of all integer programming problem by Gomory method.

Maximize

z = 4x₁ + 3x₂

Subject to

x_: + 2x₂ < 4

2x₁ + x₂ < 6

x_p x₂ > 0

and are integers.

6.    (a) Show that in a Boolean algebra, for

any a, b, c

((a V c) A (b' V c))' = (a' v b) A c'. (b) Find a Boolean equation for the function f = E (000, 001, 010, 011, 111).

7.    (a) Explain in detail about tree searching and

undirected graphs.

(b) Find the phrase - structure grammar that generates the set

L = { 0ⁿ/ lⁿ ; n > 0 }.

8.    (a) Design a finite state machine that performs

serial addition.

(b) Prove that an (m/n) encoding function

e : Bⁿ > Bⁿ

can direct k or fewer errors if and only if, its minimum distance is atleast (k + s).

6.    (a) Show that in a Boolean algebra, for

any a, b, c

((a V c) A (b' V c))' = (a' v b) A c'. (b) Find a Boolean equation for the function f = E (000, 001, 010, 011, 111).

7.    (a) Explain in detail about tree searching and

undirected graphs.

(b) Find the phrase - structure grammar that generates the set

L = { 0ⁿ/ lⁿ ; n > 0 }.

8.    (a) Design a finite state machine that performs

serial addition.

(b) Prove that an (m/n) encoding function

e : Bⁿ > Bⁿ

can direct k or fewer errors if and only if, its minimum distance is atleast (k + s).

Attachment: annamalai-university-2008-b-c-a-computer-application-15482-1.pdf

Earning:   Approval pending.