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MGOC10H3 Lecture Notes - Tinn, Zirconium, Lur

Management (MGO)
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MGTC74 Analysis for Decision Making
Lecture 01
Chapter 2 - LP Model Formulation & Solution
Example - Giapetto's Woodcarving*'$ Wso{iearving, Inc,, rrurnuf-asturi.s t1&'o types uf wc$den t0ys: soldiers anel tmins'
A sotdi*r .*elis f*r $?? urrd osus $ I * wn*tr cf rar,v lnaterials. Xa{rli c&ldisr that is Eranufa*iured
inclreases fiiap*i{*'s virriable lab'r:rsnd cvesh*sd c**tsby $14. A train *ells for $31 rnd
uses $g wnrth af raw msteriatr*. Ench rrain huilt in*reases Ciapetts"{ variable lnb*r and
$vedrend casts by $10. Ths manufacture of w**rlen s*ldicrs and trains requir*s l$'o types
nf skilled latrar: cflrpenrry anrJ finishi$g, A stldier requires ? hours rf finishing labor *ncl I
hour of c$rp€rtry tabar. iq *'ain reguir*s I hr:ur of finishing und t hnur sf carpefltry lab*r.
[ach rveek, *i*p*,*o can abrain all the ne*ded raw msterial but r:nly l'00 finishing haurs
snd gfl wrpentry hnsrii" Denrand far trai6 is trnlimitsrl, but at most 4{} sQldiers aie b$r-lght
earh lveek-, siapeno w&n$ tt} m$ximize weekiy pr*fit {revwues * cnsts}. F$nnulatt a
nraihernatiml nrodel cf Giape tto'* sliu*tinn thal con be us*S to maximiee fiiupetto"E tFcekl,v
h{'kfJ {llterpiculs prorlu**s llr:* ;:rr:rr}uc{s t}r;rl i:-r* **ld i!$ ri}!v ln*tr:ti;ll* t* {*lnpimi*s ma*u-
f+l*tur.-ing hllth rr.r:rpc a*r"I Xs*ndl'y cl*t*rgerrls, $;ls*rl {Jn lln ;rn*l-ysis rrf r:u*r-tttl ittl'rlltlr;r3' t*r'-
*ls ;u'lrJ p*rr*nri*i iierirlrnd iul tl:* t*ming mofith. i'{.t*l}'r n;itr!ilglr:t}lt'tll :il}e('iticil thirt the:
c*nlhinr:$ prt:rr[ui.:tiuc i-*r prlrdui:I$ A fi]]il [] tnttst tr:tal a[ least .i5{} gal}t:r:s" S*;riu'*l*11', a
nliijrrr {1rsrr)mer''s. r}rtler lirr lXi ggtlkxs *f prc'duct A nrurl als* hr: slttistr'i*tJ. fn.rrlLlr--t i\ r:*-
quilus ? ht:rrrs r-if prcx*csxing tinrr: p*r g*ll*o i.tnd ;:r*dnet Ll tt'quire* I htrur *t'i:nrc*ssiltg
rilrlr: per gall*n. I;clr lhr c.l$ling mrrnth. frlXl hclr"rrs *f'pt'*c*ssing tiurc $r* i:vliiltlhl*, h:t&I-)"*
*hj*,*tiv* i* tt snlisl; ll:e** r*rqnir-*,rs*nts at * ntirir*ucn t*tftl pr*dtreti*t: ct:lsl. Prrnlu"-ti$n
{r:sls i}r,* $? per gallt-rn tirr irrt-xitri.:t i\ anll .,S.} p*rg:arllr:n lur pr*dtt*t l}.
For every gallon A produced at least 3 gallons of B must be produced
Example - Dorian Auto
il*iiari*r\ufo nrxnufactilres luxnry sxrs and tra*ks, Th* company believes that its most
lik*iy cu$tomer$ are high-ine*m* rvolrr*$ and msfi" To r*sch [hcse gr.oups, Doristt Auttt hlrs
smb*rk*d on &n *mbiricus'fV adve*ising campaign nnd hss cl**ided tn purcha*e l-lnirrr-lte
ccrnmercial spots *n twCI types of progr*fil$: urtnedy shows nr:d fa rball games. Each
r;nmeely sonm*rcial is *een'n'y 7 millicn high-incnrne rvilmen anrJ 3 rniJli*n high-incanre
rnerr. E*ch f$otbrill ccrnmercial is *{een b.v ? lni}lien high-incnme lvCInlen and 13, miilio*
high-in*rne *len. A l-mirrut* c*mrdy ad c*sts $50,0t1$. end lr l-ninutc ftmtball ad ccsts
S l00,ii0*. Dctrian r.l'ould like rhs {*lnmsrcie}s to be xe*n by at lsast 28 rriltion high-ineorNe
r,$om€fi and ?4 millio* high-inrnrne ln&n. tlse linearprrrgr*mming to dat*lmifis h*rry llorian
Auto can mf,{t ifs edvertising rnquirenents at minim$tll co$t.

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