University of Mumbai 2007-7th Sem B.E Electrical and Electronics Engineering Introduction to System Design Old - Question Paper

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Irfr odtL    io Systems

DCS \*tO CD-6873

(OLD COURSE)

{3 Hours)

[Total Marks : 100

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(1) Question No. 1 Is compulsory.

(?) Attampt uny four out of remaining six questions.

(3) Assume any suitable data, wherever required but justify the same.

a) Draw Ad-joint for following 20-port Network.

|i) Voltage controlled Current source

(ii) Current controlled voltage .source

(b)    Explain in brief linearly increasing hazard. Derive expression for reliability, probability of failure, failure density and MTTF.

(c)    Explain the term degeneracy. How it can be resolved ?

(cf) How do you recognize that an LP problem is unbounded while using the simplex method ?

(e) Pertaining to Simplex method define following terms :

(i)    Surplus and slack variable:;

(ii)    Basic and non-basic variables.

2. (a) State Toilegens Theorem and prove be the same. Also stale the applications.

(b) For the two Networks shown below :

Prove Relations :

1- (

hfBTWORkS

Where V_KA and J_KA are voltage and current in Network A respectively and V_KB and I_K6 are- voltage and current in Network B respectively.

3. (a) What are the advantages and limitations of graphical method to solve LPP ?    5

(b) Use graphical procedure- lo identify :    15

{*) The feasible region

(ii)    The region where the slack (or surplus) varaible are zero and

(iii)    The optimum solution for LPP problem given below ;

Maximum f = 3x + 5y

Subject to :

(0 x < 4 (Ii) 2y < 12 (iii) 3x + 2y<18; x > 0, y > 0.

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heim WO I*).

A. f) Find the basic optimum feasible solution of given LPP by Simplex method Maximize Z = 2QQ0X, + 3D00x₂ Subjected to constraint;

6x, + 9x₂ < 100 2x, + x₂ < 20 x, > 0, x₂ > 0

(b) Us3 two phase Simplex method to sove Ihe LPP given below :

Maximize

2*i

5.    (a) Explain In brief

(i)    Unit Redundancy

(ii)    Element redundancy

(iii)    Stand by redundancy.

(b) A system consist of four constituent elements A, B, C, O with respective reliability of 0-98. 0'S6, 0-99 and 0-98 respectively. Whal is reliability of the system ⁹

(i)    All are connected in series

(ii)    All are connected in parallel

(iii)    Parallel conr>ection of A and B in series and C and D in series

(iv)    Series connection of Parallel combination of A and D and C And D.

6.    Consider the transportation problem with Three Warehouse and Four Markets

	Ml	m2	m3
W|	- t_a	13.	15L	IX
	Us	"Lit	U	lit
W5		Tl	L*
OfcMAWD-*	ft	3

Find out the basic feasible solution of the given transportation problem by VAM method and use further u-v method to improve on initial basic icasible solution.

7. Write short on :

(a)    Decision Theory

(b)    Monte-Cark) Simulation

(c)    Big M-method for solution of I.PP

(d)    Comparison between dual and primal and utility of dual.

20

Attachment: university-of-mumbai-2007-b-e-electrical-and-electronics-engineering-51210-1.pdf

Earning:   Approval pending.