INDERPRASTHA ENGINEERING COLLEGE

( 4"' Year. 8th Sem. Mechanical Engineering - A & B )

M.M:60Time: 2 Hr

(Solve Any six Ouestions. All Ouestions carrv [qual Marks)

1) A toy manufacturer produces two types of dolls; a basic version doll A & a deluxeversion doll B. Each doll of type B takes twice as long to produce as one doll of type A.The Company has time to make a maximum of2000 dolls oft)?e A per day.

The supply of plastic is sufficient to produce 1500 dolls per day & each typerequircs an equal anount of it. The deluxe version is type B requires a fancy dress ofwhich there are 600 per day available. Ifthe company makes a profit ofRs. 30/- & Rs50/- per doll respectively, on doll A & B, how many of each should be produced per dayin order to maximize proht? Solve it graphically. (10)

2) Bricfl;, explain tbe mecbanism & managerial significance of post-optimality analysis/Sensitivity Analysis. of a sinrplex linear programming solution. ( 10)

SiWiial is Operations Resd.nuir? Erpiain l eiiy ihe differenl pliases .ri CperaiionsResearch & general method for solving Operations Research models. (10)

4) What is the difference between a Transportation & Assignment problem? Use Vogel'sApproximalion to find the initial possible solutjon ofthe following problenr: (10)

(Pro)

Source

Destination2 4 5 Supply

I t6 r6 tl 22 T7 502 t4 t4 1l l9 i5 60

l9 l9 20 23 18 504 2l 21 30 l8 20 50

Demand 30 30 70 30 60

Or

Explain general structure ofa linear programming problem using mathematical symbols ,& , Minimize: Z :2Xr+ X2Subject to I

Xt+ X: >= 1

Xr+ 2X: <= l0 rX' 4 'L''. -\)* x, '- o. x, >= o "r

(fir, \

Use $aphical method. \ "

5) Using Simplex Method:

Maximize: Z: l0X + 5Y

( 10)

Subiect b:'l!"

4X+5Y<=gg5X+ 2Y<= 120X,Y>=0

6) Explain Dualitv in Linear lrogamminp & obtainprogr:arirnring ploblem €solve by srmprex meinod:

the

(10)

dual of tlre following Linear(10)

MinimizeZ:Xr+X2+X3Subject to conshaints: Xl- 3 X2+4& >:5;

Xr- 2 X2 >= 3;2Xz- X: >: 0:

. Xt, X2, X3 >:0

7) Explain Objectives ofOperations Research, along with Scope & Charactedstics. (10)

a,

Op<"sk6"ro (ro era.\ Lz'."\ ) e-*.. ,

r) Gc,\N< * d**\ A,aes.^- f^[.^*" t$ P^db!s."ir\q*,.t'*rse'" z "- \o^, t3o u ,- 4rlo4"

€'tqP'4 to .

)*,'t5"tz- +tortg -< los

2,q, + 6t,-r_ t3f6 <,looVrt r +zX2-+ zoc5

=+ 6oo -

€Lt t i-,\Va

z) 0rt4t1 e.Pt.L jkq 'vnec}'o-r'r'uvn

"1 f""'o1li*.'"Uk( t.rn"'l7d,-, { cL

S,il'si.

e^"i

f ur.unSeus\S'/^qfO*^.p[err.t $teq* fl*y"^'"'

t) Ghiv" ttlo d\d of dt^a d{t*i^t ll)aer.n

0nt'bt"n & ,So\,,re L, S4-n !le\oq;*St.1t 2{"r.'tz +qi

- €^th"* tct (e^^e'qs*fa\ o,, - 3uz- *yu375

tl1 _zNa2-3z*2, - 4z >o

Arl Xz- ,4b ?.. O

4\AR,"l

c

lds

hs.*

t loso".+"{r,\ hot.re- c{.q{qttat.,J, crn$rrrr{et\f^ra St\,hlftu

Y,5:ffi.n-,\ hh',rffiu!*3 I l."7..'L .t .[ro..,^ tdi^$ CAIkoD:fr'u R ttlsa d*-au";

- &*T 6 ss$^{^!41 \cur.^ {

P*F * on- \x*1 A io 0,a r "" t-Clvrr b*Y g ; 0"u lr. SSSr..w.l'^-1 tha\ $-c Cw", Ss.k-

ctN t$"l l^' grci.ttu,ho\s'rv^0\ 1 '-n.tl, SO *pt.rtuwt'oda-^a $r. s$tlru

nnArc"l (b .9$.,.r< \ $"d

aiShu'"' *hq ^*

idw^ny-:tlq .r.nA,{,t1tu"/1\rwr

S}.ottsL be-

$si- ft$l,nca'\P*$<

u

d- tr4our',"i1e- 7=' Z-Ar-t Xz*

&,bie$ te X 11 2Xz4 Js' \ I1112 a (

Xr -- Xr- z. 2Xr - LAz-1 I

& x,)o, xz-)o

c]"tt A

B

(-

F\

V

l? 8 ',

r{,Qr,'r|2clst5 lt rS 11 l{1t2\}?rtr2Ll\ I) lL tt lS

f.-tl"O, lu" Crr:o\a''"

r\hr tob$

$s'S ,rrr.-it,1"i5e/)

I;"1 'F; -+"" rs cs'*1odsol (""**fl*f, 't:r,.0 t.+;

idtu lA\\*;,. \A^''(\-

s\ ft", i''^\se5iq$'\ \'* JdR^* Y::-'"*"#u-, *:l :ff ir-rul};:uss**fl+.ffiJ'$uSil'Ht*35 1ars.v'ln.

o* \, L & 3 o'D

Fr.'. Fcrtforlrt C.p.\AtL'" $e-oln's

Fi^d b'$4* c'!sat t

$e"ltoti"q^ Ir'o^hil '*

o

ft

b

bR

6

&* t3-

'W*- I

&7at\.et'mQ"t.

r-iI

Cf^shr"- /r^rr, ,,j'' [rve-osr) (H:ffTt.'^^p'e$'\ AAssrf^E^nGoq",*\ -MB

T\- ts\il*! "md^il gh.r,5 :kN p"{..f eo^'""t !ii6\$ Sd,t,l ?zrr/rtv!. Lrra 0^\ f , , ?2, 0 3 **

\ wo,it

,j^ lU"* \"^".S SoXu uN\e- Lt, zr-{ Zj

r-c,re.o soff.o,i *]A ai.o.'l,t Uu ttn""L^^u^-r' Atao'lrarhlrf

1r.4& " o lt'^' Q;'" '?Y'>2--"la*>2"5

Y="tJr) A.m,-i'.o ddir 6F*aA Ss[ura& q Jeq "S,"^noe#rm-

$Aqtffi* & .tO" JC& cpil',qolp" , -Frcr\ghr^ ; co.t'r sbi^

P'

P.

?

?\\.^w{^+,&[}d-ot-rv.d ust r cL ss-ran oe,^!jc\ $^D\r\a b{ &rrd}9h e4-r I - -l

\r^u-.-r , g 6j loie-Iiqq,h.r &

' / i,rr ^\l l r _.-r

3s ?ob

\^nfY\

7^;" ur* +-t ^t"t, Ss[' i'"'

o*'ipt-r"l &.q."*J" "fl" ^'

r - ' / SsU'I'$-.' €*"et^ )

L q -Y fr.\, 'oe ytrB\ , br{04 ,

C-) h, Lp.O , c+ y [q f '

6""f1.-lr\ tt ) Ul\rr! $n.l Hr'yc*;o"- "ihtt-. \ pn_l,no W,o^l Ayd^""{M-ods-\ r- cr Y<ru"li .-t i $*^ntJd^- .r.,.dq{

"ql 0p,,-,t-g 36u t^[t'"y p*ld'$"u;* h..****-u^r\4 vAM.7"t $" Et*ll,f, "^*l sTi,"f gi!'{ $^idt., .., \r ,. u {J

uJonqjv:n-r e_

W\0!^!t P-{-o

( O*1. /*qh^r-^"^ iA', ly'^---.n1c''\-- l"rt}lno")- '--+ O $od

- Atlqtr^b*{{-d"\. \L P".'ll - SOvo "r'a!,; ' '

,o

9r \r ''

OL

lg

lqloq

eIb-q,(L-P,to\ rq.rll,i-

C.- A<lJ"r'lr

"^toJ _

\'\l"-t}nl*

Ntluhh^.t

I c

4t1=

?o7,'1 o

2Dtl

l2

rVtlL

r8

6oo

6oo

6o,c'|otr Yop P,ro

^a "^f-evrt r""6trM *-w; fi*lrd**

x{\ n-' d,Ju ir.o N\ "\., Lrpl

CI.Y

q3

..>

s(

eD

r8

lDt(

(

jr 6.

1-o l^ 5o

t.o

{o r rr*plW^,,* d\ Iro I *-[i l*rn' + g x SS +\xlo

lD 1(xlSt3ntSraxSst-_) r{ro1 11--; t[8s) e

q +z-[1.n ,, zl30s) ,. .13, | (Js\ I p- +tLts)ldx,,/"r.1 J

?) Ael",,,..'*- *ye sfJqi.cn{ o.^'7v"-tt h , *

h\br^44 $rL{ern - T\<-doiq,rtao.t to^ll-u"'^t vtlci.'JzB^'f' cov"ov*

won)"L i ou\] -f

*u'["n bt eq,^nqi- v!\)\ilc^t

job ,4)l(r

c'l O ro

I Q- 3gI

r,.r.rltoa- o.5a 5o\9 4o$o $ootD

,t42o 3o

[o ton \Jg[F ->ql.r.r.\/l$na

I z I \Asw

^ -42'Ao- -) "-'l4+tJ

?9