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Lecture 1 & 2.pdf

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University of Toronto Scarborough
Management (MGO)

MGTC74 Analysis for Decision Making Lecture 01 Chapter 2 - LP Model Formulation & Solution Example - Giapetto's Woodcarving Wso{iearving, Inc,, rrurnuf-asturi.s1&'oypes uf wc$den t0ys: soldiers anel tmins'*'$ Xa{rlic&ldisr thatis Eranufa*iured A sotdi*r .*elif*r $?? urrdosus $ I* wn*tr cf rar,vlnaterials. inclreases fiiap*i{*'svirriable lab'r:rsnd cvesh*sd c**tsby $14. A train *ellsfor $31 rnd $g wnrth af raw msteriatr*. Ench rrain huilt in*reases Ciapetts"{ variable lnb*r and uses and trains requir*s l$'o types $vedrend casts by $10. Ths manufacture of w**rlen s*ldicrs nf skilled latrar:flrpenrry anrJ finishi$g,A stldier requires ? hours rf finishing labor *ncl I hour of c$rprtry tabar. iq *'ainreguir*s I hr:urof finishing und t hnur sf carpefltry lab*r. but r:nly l'00finishing haurs [ach rveek, *i*p*,*o can abrain all the ne*ded raw msterial snd gflwrpentry hnsrii"Denrand fartrai6 istrnlimitsrl,but at most 4{} sQldiers aie b$r-lght earh lveek-,siapeno w&n$ tt} m$ximize weekiy pr*fit {revwues * cnsts}. F$nnulatt a con be us*S to maximiee fiiupetto"E tFcekl,v nraihernatiml nrodel cf Giape tto'*sliu*tinn thal proftt. Example-M&DChemical prorlu**s t}r;rl:-r**ld i!$ri}!vln*tr:ti;ll* {*lnpimi*s ma*u- h{'kfJ {llterpiculs llr:*;:rr:rr}uc{s f+l*tur.-ihllthrr.r:rpc*r"Xs*ndl'y cl*t*rgerrls,$;ls*rl{Jnlln;rn*l-ysisrrfr:u*r-tttl ittl'rlltlr;r3' *ls ;u'lrJrr*nri*i iierirlrniul tl:* t*ming mofith. i'{.t*l}'n;itr!ilglr:t}lt'tll('iticilirtthe: gal}t:r:s"*;riu'*l*11'a c*nlhinr:$ prt:rr[ui.:tiuc*rprlrdui:I$A fi]]i[]tnttsttr:tala[ least .i5{} nliijrr{1rsrr)mer''s.rtlerlirrlXi ggtlkxs *f prc'duct A nrurl als* hr: slttistr'i*tJ.rlLlr--t:*- quilus ? ht:rrrsr-iprcx*csxing tinrr:p*r g*ll*o;:r*dnet Lltt'quire* I htrur *t'i:nrc*ssiltg tiurc $r*i:vliiltlhl*h:t&I-)"* rilrlr:r gall*n. I;cllhr c.l$ling mrrnth. frlXlhclr"rrsf'pt'*c*ssing *hj*,*tiv* i* tt snlisl; ll:e**r*rqnir-*,rs*ntst * ntirir*ucn t*tftlpr*dtreti*t: ct:lsl. Prrnlu"-ti$n {r:sls i}r,$? per gallt-rntirrirrt-xitri.:tll.,S.}*rg:arllr:lur pr*dtt*t l}. For every gallon A produced at least 3gallons of B must be produced Example - Dorian Auto il*iiari*r\ufo nrxnufactilres luxnry sxrs and tra*ks, Th* company believes that itsmost high-ine*m* rvolrr*$ To r*sch [hcse gr.oups, Doristt Auttt hlrs lik*iycu$tomer$ are and msfi" smb*rk*d on &n *mbiricus'fV adve*ising campaign nnd hss cl**ided tnpurcha*e l-lnirrr-lte ccrnmercial spots *n twCI types of progr*fil$: urtnedy shows nr:d fa rballgames. Each rvilmen anrJ 3 rniJli*n high-incanre r;nmeely sonm*rcial is *een'n'y 7 millicn high-incnrne rnerr.E*ch f$otbrillccrnmercial is *{een b.v? lni}lien high-incnme lvCInlenand 13,miilio* high-in*rne *len. A l-mirrut* c*mrdy ad c*sts $50,0t1$. end lrl-ninutc ftmtball ad ccsts atlsast 28 rriltion high-ineorNe S l00,ii0*. Dctrian r.l'oullike rhs{*lnmsrcie}s tobe xe*n by r,$omfi and ?4 millio* high-inrnrne ln&n.tlse linearprrrgr*mming todat*lmifis h*rryllorian Auto can mf,{t ifsedvertising rnquirenents at minim$tll co$t. [z-( \ chod-v-2- Lf pr,cl}\ s+o.J cl.,'-.-J^,JWS e) 9pe-t (e Ccn s 1-a l,n*fs ,.1 "SlJ ) 5 b^ ne-st^icf lons sc\ v 6.-,)aLte.s P>. G;,p^?"(J- van'a,bUl: vaa-iabl*Sl-Ar,Jksct;,6u -'l',l"r^x$* J- ,bp m..olt ferfab^ 4, = d vI Sv[Mb{S ,t^'A e^t/L '*4/* ac=i""1. rirni,rs t tnon(,-vvur"fu' tvtanY'"u"?''/K"l o> tv1,\nit-,iLwslt Kbk '),Jpra/","f1V"/ /L" -1[,;, is*tfu'(4L oL,v^-rl*- fr*,,*vr. hiopo'ft-t of'-rilt"/^-A'v^ k'lt h4otY Pffi ' = d1\ts!:'-,!t::I-"7 g+ry ^u%P.ff' geArr'l,^L 7q'b,^alea>'L /^L- 3a, +? %t oblt/h\uu : v|\ny? = 3'v, +) Tz fuczh\'r tf :r',,r-n''>^1 Awrc a'7o"-'r7-/z\'-r*'/ ''^1,,!,\'r9,'.,u l*grain/L / +he^ )-e u "" Lo7^.[,a.-,linu notJ,ro,-* *4 *, *' ; ;; ^- ]o' ;r:l;,it:'t'ii3il # ^" ^" "*r"rl;"tgl,'t OX'+12 s (w Y,,Y277o .t[ v,,\z rta,$+.h*+t,rM : q/ t'tosfQo 3o/do'6 s"tJ We hn'*tinf-f+rk|vartgwVwtn'f ) S a ,1,( X Q v\o.1.: Z= 3x,i).x: vn or )X ,Y:-{}, Y Unre'dt>i*4 /4ts,[t^, ,/r 4*n ur [n* ga'nrp-n&rr..t(4,tS,|Jr,UtTUa)7o/ Vwn-LlrctP*f**Y- Exo^p b-, DerrT,ba-ar;oL(z- /ar,a/0a +/*t /qrr;lU +/^,.6/*rrhos T,D bz ,*/n O be/,h'yp fun4'an, iyeY/ /zoBrlr*w/r4, warvr a rantnizL Qraf't, eu-+p4, p//o/1,)&. ar ^:,rd*buag*, ?re eom?- 7*na,oa o/ t/.e- v^rr'obLs #@ vl4'a.nuu : lnhx A --JXtfLXz 1ra,h fur&'0, A U4rai,v( caryattjlww< : Xr*Xt(N
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