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and Rott

No b b.

f

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(sEM. Vl ) THEORY EXAMTNAIION 2010.11

OPTIMIZAI'ION TBCHNTQUES IN ENCINEERJNG

Not.

:

(l) [email protected] qutions. (2)

Athpl

rtr par6 of

firt qBrim ad

lhE

@h mddns

tBo pds liom

queniors.

qu6tid Mies 14 mk wlile loaining qu6rim €ry 12 @ks crch.

(3) Fiur

.

(4) A$umc suiable

dala

ibe

hi$ins if tuy

(a) DificmkaE b.tften ConB polyh.dron dd polrropc. O) What k fi. sisnirrace oflases. nultiplieE 2 (c) D.6nc a saddle poiDt ed indicatc irs sigdfituc.. (d) what do you undcs!.nd ,iy noDliD.ar l.a.r squar (.) Whd

is an acliv.

(0 Conpac h.tvccn D.6n

lhe

cmhinr

?

Euler ard nodified

orelatim cmmci.ni

Ella nerhod:

(2'7=lr)

(.) l]l@

dd cl*siry$.5t ion rypoin6ofrh.followins

nDdid:

(x,,, o)

= x,r+ 2:r

!+ 2!r -2!+!+e

D.bmim wLdnoth. folosiDs irdions

ft

c@q o.

r(i,,i:,x,)=4,,'+3*+5{+6x,!+r,4 3x, (o) coridsrhefondi.sprobld _

Mininirc f=xL:+ 4,+

2x,+15

:

!2

$bjerto

\:0,!>0,xr>2 D.i.min

wllernu fte Kuhn-Ttut . conditions ar€

' $n6.datlh lolwing

poinL: x, = 2,,q= l, x,= 2.

(2x6=r2)

3.

G) wriicdc d.Fs

in Gendi;

Aspnlnn.

(b) [email protected]@s=

(l,l)rd r[.

lh. nuciion {x,, EF 2t: + Conpar. n vilh th. dir.c.ion VJ

de3d

ror

D€siherhe Eula'!.th.d b

poini (2,3)'

t: .!

2x,

!

i.

+ 4.

x= (2,3)r,

slw o initirl vnlepDblm, (2x6_r2)

TLl width of r slot on . dlsliu forying is.nom.ly disrib*ed. The ry.cificaiioni of tL. dol vidli is 0.900 I 0.005rhe pruh r = 0-9 ed 6 = 0.003 e knM toD p.st dp€.ide in pmddion F@$. What i. tI. paan

olsdp

ldging ?

o) Expl.in rie cqfiils posl?lmilglri$Lh

planc Circ

n

rhod Ds.d in

irlcg.r

d.xrqla

G) Usils SiEDL{ arsdirLn slw rhe fonovir,grmblm: ,Mimize, = r+2y sbj.ct io 3y,+ 2y,< lz2,t,+ 3y?6, y,> 0,

y;isuffiriict

n

insicr

(2x6.lr)