RTU 2016 Question Paper Semester IV Electronics and Communication Engineering Optimization Techniques

*qlt;s{ :"r=

RollNo. Total No of Pages: I
+
CN 484L34
F{ B.Tech. IV-Sem (Main & Back) Examl June-July 2016
+
EI
Electronics & Communication
$ 4EC5A Optimization Techniques

Time: 3 Hours Maximum Marks: 80
Min. Passing Marks (Main & Back): 26
Min. Passing Marks (OId Back): 24
Instruc tions to Candidates : -

Attempt any ftve questions, selecting one question from each unit. All
Questions carry equal marks. Schematic diagrams must be shown
wherever necessary. Any data you feel missing suitably be assumed and
stated clearly.
(Jnits of quantities used/ calculated must be stated clearly.

Use of following supporting material is permitted during examination.

(Mentioned inform No.205) r, . .

1. NIL 2. NII-

UNIT.I
Q.l (a) Define the following: l8l
(i) Design vector,
(ii) Objectivefunction.
(iii) Design constraints
(iv) Constraint surface
(b) Define optimization problem. Explain it with physical example, t8l
OR
Q.l Write a short note on the classification of optimization problems based on various
parameters. t16l

l4E4l34l Page 1 of4 1428ol

e'2 (a)
fl.,flffiffij:xffi:fj, .n"rffiwing iinearprogramming probrem
has
Minimize f
=-3xr-2xz tl0l
Subject to x1 _ xz (
I
3xr-2xz<6
(b) Write the dual of
the followi,,o linear
ri-^^- __-_
Minimize Z
programming problem:
= xr* *r*''ll*'ng [6]
Subject to x1 _ 3x2
+ 4x3 = 5
2x, - 2xr< -3
2x:. - xs> 5
and x1, Xz ) 0, xj
is unrestricted in sign

Q'z (a) use Revised Simplex
Method#rotu"
rvrvt'('(r r'o solve ,t" rnr^...:_- linear
the following ,.
probrem: programming

Minimize Z- xl+ 2x2 t8l
Subject b 2x1t
5x2 > 6

x1* )r2) )
and Xr, xz > 0
(b) Find the opdmal solution t8l
of the following line
Max Z = 15x1+ 45x2
programming problem: v
Subject to x1 + 16xz<240

5x1 + 2xz< 162

xz<50
and Xr, Xz 2 0
Further' if Max Z
= LC: *: , j = r, 2 andC2 is kept
much cr can be changed fixed at 45, determine
without affecting thl how
auove solution?
[4E41,34]
Page Z of4
[42801

UNIT.III
warehouses at D, E, F and G'
Q.3 A company has factories at A, B and c which supply
optimum
Unit shipping costs (in t ) are given in the following table. Determine the
Approximation
distribution for this company to minimize shipping costs by Vogel's
Method. t16l

From To Capacity

D E F G
,t
A 42 48 38 37 160

B 40 49 52 51 150

39 38 40 43 190
C

Demand 80 90 110 t60 440

OR

Q.3 Four different jobs can be done on
four different machines. The setup and take down
below
time cost are assumed to be prohibitively high for change overs. The matrix
gives the costs in rupees of producing job i on machine j: t16l

Jobs Machine

M1 Mz M3 Ma

J1 5 1 1l 6

l2 8 5 9 6

J3 4 7 10 1
a
Ja 10 4 8 -')

How should the jobs be assigned to various machines, so that the total cost is
minimized?

Page 3 of4 [42801
14E41341

Q.4 (a) Prove that L1= (0.618)
o-t
Lo, where k is the number of experiments performed
and L1 is the length of the interval of uncertainty remaining at the end of kth
experiment performed in Golden Section Method. . tSl

(b) Define the unimodal function and give an example of it. Also draw the Flowchart
for Fibonacci search method. t8l

OR

Q.4 (a) Minimize f (x1, x2) - 2xr2 + x22 by steepest descent Method with the initial point
(1,2)r. (up to three iterations). tSl

(b) Minimize f (x, y) = x'+ 2y2. Subjectto 2x + 5y -10 < 0, by using Exterior
Penalty Method. tSl

UNIT.V
Q.5 Divide a quantity b into n parts so as to maximize their product. Let, f" (b) denote this
product. then show that

fr (b) = b and f, (b) =o
5:, lzr, , (b-ill.
Hence find the f, (b) and the division that maximize it and z is one part of b. tl6l
OR
Q.5 Solve the following linear programming problem by Dynamic programming
Approach: t16l
MaxZ = 2xt +5xz
Subject to 2x1 + x2< 43
2x2< 46

14E41341 Page 4 of 4 1428ol