University of Mumbai 2007-7th Sem B.E Electrical and Electronics Engineering Introduction to System Design Old - Question Paper
[Total Marks
CO/I. U141/ VWWaiw*.
(3 Hours)
N.B*: (1) Question No. 1 is compulsory.
(2) Attempt any four questions out of remaining six questions.
(3) If accessary assume suitable data wherever required and justify the same..
I. Attempt any four out of the followings
(a) Pertaining lo the Simplex method explain the terms surplus, slack and artificial variables and llicir use.
Explain in brief methods lo improve reliability.
Explain and compare primal and dual LPPs.
Write the dual for the following LPP.
Maximize Z-15 X| (-2x24-3x3 Subject to the constraints
xi 2xj
4xj 2x2 3x3<8
(e) Draw adjoint networks for the following two port networks.
and X|'X2
M
cmpt any four out of the followinus : 20
(b)
(c)
(d)
., + x2 + x-j < 10
-x3<5
x3 >0
For the two topologically same networks shown below verify the relations
#
12
(b)
KA *KB 0 and VKD lKA 0
Where Vj 1A and VKB 1 are branch voltages and currents for the two networks A and B respectively.
lO-TL
x-t
<VWW>
|
xg |  |
|
3o\) U |  |
3A
10-n. ta.
X VWW) (+3>>
N/tfiMoA- A
3. (a) Solve the following LPP problem using Graphical method. Show the feasible region and mark 10 co-ordinates of all comer points.
Maximize F*2x, * 6x2
Subject lo the constraints
5x, + 9x < 45 -x, +x2<l
2x2<5 and Xj,x2>0
(b) Solve the LPP problem in (a) using Simplex method.
4. (a) Explain and define the terms failure rate, failure density, probability of failure, Reliability and MTTF. 10
<MS
(b) Find the reliability ofthe system consisting of subsystems with the reliabilities as shown in the figure. 10
|
->1 ..... *-> |
-=>- D - |
5. (a) Explain and define the sensitivity for network function. 4
(b) For the network shown find the sensitivity of output voltage Vq_ 16
(i) When only current source Is changcs
(ii) When only voltage source Vsj changes.
Use adjoint method.
6. Consider the transportation problem with three sources and four destinations. SQurce capacities and 20 destination demands arc shown in ihe table. Also mentioned are the unit transportation costs in the brackets.
Find the transportation cost using
(a) North-west comer method
(b) Least cost method
(c) Vogels Approximation method.
7. Write notes on any two ofthe followings: 20
(a) Two phase method of solving Linear Programming Problem.
(b) Big M method of solving Linear Programming Problem.
(c) Monte Carlo Simulation.
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Attachment: |
| Earning: Approval pending. |
