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5 Fl6t l.lt . of you. lest n.me (leftlusttfyl) Last5 dlgitsof yourStudent Number(SSN) attt )tta Buslneaa Management Examll 331 (Lst First): Name / 3.nPrc x*a" Z4 Youhave90 minutes complete exam-A counldown to lhis timerwill be projected the scrn on duringhe quiz. No"time given theinstruclor checks" beverbally will by during quiz.When 90 minutes complete, writing cease. the the are all will question Please read each carefully dirgclly and answer question is ask6d. lhe thal Youmayusea calculator the exam. Howevgr, insliJctlon lhe useof lhe calculator it8 functions be given for no on or will dudng 6xam.In addition, sharing calculatorspgrmitted. th no of is f,IE USEOF CELLPHONES ANDPDA'SAREPROHIBIIEDI Placethe answer lhe question lo askedin the boxprovided.Points be deducted answeFnot placedin the box. will for Do nol wrileequations anything o. olherthanthe answer the box. in Only student allowed a limelo uselhe restroom. willsuncnder exam thinslruclor to going one is your prior at You to lo yourretum. therestroom it willbgiven and backupon Nocommunication kindis allowed of any belween students during course lheexam.Thisincludes forms lhe of all of verbal communicalion, written communicalion, electronic and/or communiclion. I havereadthe examinst uctionsabovoandunderstand anyviolauon that ofthe examrul. will rrsult In a 3uSDoctod of academic ca6e misconducl Slgnaturo: Dat.: Do notw'ito belowthis ling Totalpoints exam on Totalpoints missed 248 Percent conect Curved score Edited by Foxit Reader Copyright(C) by Foxit Software Company,2005-2007 For Evaluation Only. in Hls lo Smith eamsexaclly a l. [32 Polnls]Marc $35,000 yarandhasappronmably $6,000 invest hisportfolio. and refumsare shownin thefollowirEtabl6: investment altematives lheir expoctd lnve3tmont B D6criplion ExoctodRotum 6.5% lnwatrnont De6c.lptlon mutualfund Unity Libgrty mutualfund Moneymarksl ExpactedRstum IRA(retirement) Employe/sretirement plan(relirement) Deferaedincome (.6lirennt) 11.9v. 9.5% 4.80h 15.8% 18.0% goals inveslrnent areas follows: Marc's Goal Weight 1 Descriptlon lnveslallfundsavailable. 25 20 15 15 10 2 3 rotum dollars in of$1.200. Achieve minimum a annual plan. invesling than3%of sala.y omployer's les6 in retirelnent Avoid in market. Avoid investing lhan10%ol thetotalinveslmont lhe money less Avoid investing more lhan 25% of the total investmentfor retircment plans. Avoid investing less than 50% of the total investrnentin norHetirement plans. 6 10 5 7 Avoid investing more than50%of thetotalinveslrnentmutualfunds. in programming mlst b in linoar fomal to eamcrodit. DO All Formulat a goalprogram. NOTSOLVE! constraink as vadables thsamount each for in investment. Use'A','B', "C","D',"E , and"F' as decision 7, 4lhrough thinkratios.l lHint Forgoals ObiectiveFunctionI,, porrtd lllnlmize ?td,- + ?*cl,r + 2-odl +l5d{ + ttd{ r to d{ + to dl +s d.,+ Conrtralnk I,, poiats each, Irl lzl t3l L+['rc-]-r+F o.ousA , o.t't I + d,- - J,'= toccr + O , r 8 o c . 1 -o , t t j \ iO,ogflt+ OoqtE + Ci -di=rra + A * B, c B r d. -di = roso lal -o.roA - o.toA - o,roc - o.tOD - o,ro *o,1oF tq a,1sA ro,1sg , a?s.C -o.zSD -Or25V - o,ztF rd;-d; = D + di - ds' --o t6l -D,sD ^ oJ;|rn - o.-rDC- +- osu'l A All daclllon va.iabl$:0 +o.sb'- + qsaF + d" - J,i = o m - o.s)h - o,sD, - o.sDc ro,s'DD ro,SD\,- - O.5-DF .F Cr- - d; =g Do notwritebelowthisline 2 f30 Polnta-- 10 poin,r.EctrJ Dteminohe initial golution foasiblo the using Norlhwst Comsr method. D6i6rmine Inl{lfeaslblo the solution using mlnimum costalloction melhod. x z Capaciues 10 45 lr1 B L11 Y Ln l5 25 L1_ Ll9 Ltg '?41 L Lt. l4 t- Lr. L" Zo 't5 30 D t3_ Ll lo 25 L: LI Domand3 25 Whatis thevalue thetotalshipping usirE of cost the Northwesl Comermelhod? 25 Whatis the valueof the totalshipping costusingthe minimum allocation cost rnethod? I l-,-:g-l lnU< | UO Determine initial lhe feasible solution uging Vogel's (VAM). Approximation Method x A B z L:_ Capacltloa !1 L" x !_ Lr. X tiI t: l0 45 I r)j- 7 x 2a Lt0 zo(D- c D Domandg ll1 l8 c_ 7 25 25 til x L: L,t t5 30 t 5 @t, L. X 25 25 lY t3 -3 3L Whatis thevalue tfietotal-shipping using of cost Vogel'sApproximation Method(VAM)? az z -I | L-.-...LJ <ra Do notwritebelowthis line 3 problem lho f30 Potnls, Formulate transshipment at tho rightas a linearprogram.All decision have format whele isihe the AB A vadables should node g is thedestination and node.DO source mustbe in coarecl NOTSOLVE!All constraints fomat to receive credrl. linearprogramming Function Pointg Objective I.t Minimize .r- z,+F i --l ts* + Z1'e r18F +1 8L, I cc r bcF +- t r + Let'r f*l- +teA_, LtK + +FA * SFr+ 3 Con6taints Poi,rrseach, 12 Avr A?, AA 8c- +-BF t 1 roo 8= < Zos a1- -o -FF _-<) Qs" cF r ck- < sl)D cr- c_ - e)+ 'tzl:'fft'rr- t+ k. tISrrr}- 4l-.."1a + A-{ > ?-to DT r eD.r F-r C t< r t-.1.- r h.All D.cElon Varlablos:0 ,- (o"> Z 3oo can [5 Polnas.ach] lf warehouses onlypocess mustbe 200 unitseach,whatadditonalconstraints formulalion? addedto the abovelinearprogramming ;-r- 4 c-r- c < Do notwiite belowlhis line 4 Edited by Foxit Reader Copyright(C) by Foxit Software Company,2005-2007 For Evaluation Only. in I20 Potnfs, Giventhe nelwork lhe ight column, determine maximal fromNode to Node lhe flow A E in andputtheanswer theboxbelow. 7 XXXX 7 g Answer: 7 Thetable is blow toryourwork ll is notgraded! Theromaybe extraboxesdepending your on selction paths. of Path 1o A -g-e A \l 3 A -o-E 2_ A-t -c- e Do notwritebelowlhis line 5 in [25 Porrtst Giventhe network the rightcolumn, program solvefor maxirnal tormulate lineaa ihe to ffowfromnodeA to nodeE. All decision variables shouldhavethe formatAB whereA is the sourca node B is thedestinalion and node.DOl{OT SOLVEI.All constrainls muslbe in corecl linear programming formatto receive credit. Disregard any decision vadablesthat zeromaximum have fow. Function Pornfe, Objoctivo Ia Maximize EH 1 ArcFlowConslraints PointeachJ lt As=s *c 9r C8< r C643 0 Ls s4 Bc <7 Dq< a 5r--( I B <'( (..b <3 l Balance Constrainb Poirrtseact, 12 \A r G:A - l{5 -,/tc-lt'f ---O :o ),$tQB - Bc-0q --o At'8c * Dc -c4 -c6,- q6-/+D+ sD - bc - 1r.._'e Be t<,e r Dc- - 5:'4-D Alt Decision Va.i.hl$ >0 Donotwritebelow line this 6 [20 Polnts- 5 pohr|s tot oachbox, Givonth ntwork theight column, in delemine shortost the palh fromNodeA to eachothernodoandlnJllhe in answr theboxes below. AtoB AtoC (. Edited by Foxit Reader Copyright(C) by Foxit Software Company,2005-2007 For Evaluation Only. I.7J @ AtoD AtoE -1 I 4 B 7 l9l 7. f2a Polnfs, Giventhe network the rightcoh./mn, in formulate linearprogram solvefor shortest the lo path fromnode to nodeE. Alldecision A variables shouldhavelhe formatABwhereA is the source node B is thedestination and node.DONOT SOLVEIAllconst-ainls be in cofiect must linear programming formatto receive credit. Objective Function Pornta.l Il Minimiz6 2 r!J 5 \ m E t'l A r I lrr i_ll lAEr t*<- ' /Aq r-.)6/'rzAc- f IBC r fc-/r-j zc4 + 3Cb + Vc!rlDrt t3DCr ttE6+q<t! fgI Balance Constraints Poinfs eacrd Il D B Bn ' c+- D* - ,{g-4c-,45--p k Acr rC!, 6 - B* -lc-^6(' --o Ac' Dc; c- 4,a-c6-co-cr=p A DecisionVadables> 0 Do not wdte blow lhis line 7 Edited by Foxit Reader Copyright(C) by Foxit Software Company,2005-2007 For Evaluation Only. solution tilow,delermine imp.ovemsnl lhe indexusingthe [27 Polnts-. 3 PolnF for eact box, Giventhe feasiblo slopping stonemethodology eachof the shipping for lanesnot presendy teing utilizod. E L-: F G H Capaciti.s Lg l0 L-: Lx 5 L1 L1 t__: 15 B l) t__: Ls t0 25 c Ll_ L: t__:, 20 t, t:, Ll15 30 Lq 5 30 Domand3 45 30 95 Shlpplng Lane ComorPolnta Stepplng toa StonoMalhod (rroit area- not graded) Inprcvamnt Index AtoE AtoG Aulrr leel.c\lAa I rle/ te fialc-a lcr lA+ | 4<^ B?l Bdlcc., lcr I BF ? -s -3 -3 BtoF BtoH CtoE CtoH Brloal"qlcclncl+*lsu c l8 ls,elo6 la-- 0toF DtoG DtoH gp ler I hr l** lct+ le los/ BrlBal <qI cFIDF !A I ori gt I 4c.l\^ \* loE I le;'l sc lcd lc1- ArlnTtl>u 3 -b -+ -L Do notwritebelowthis line 8 programming problem graphically 9. [20 Polnk] Solvethe following integer usingth6 branclran&bound techniqu (sach in thegraph oneunit). line is Maximbe Z = 2X1 Subjecl to Xr 7X, X1 3Xz 2Xz 8Xz Xzl 5 S 10 0 Comet Polnta Obl.c{v. Funcllon V.lu. 0 16 Optlmal? (0,0) (8.0) (0,5) ( 16/3,7/3) 53/3 Yes Integersolution lruncling valuesof Xi andX2 by the at the oplimalpoint(if necessary): (s.2) | 16 Theoptimal solution not inleger. Forcethe variable lo bean integer is X, vafueand clculale nextstepusingthe lhe branch-and-bound methodology. x z3 2 Comoa Polnla Objectlve Functlon Value Optlmal? ComaJ Polnta &:3 Obleotlve Functlon Valuo Optlmal? (o,o\ f o. L) o ( o,r-) Y t1.v\ ( E,o.l lb (+,, ( o.s) 1 t-1 Integersolutions lruncating valuesof X1andX, at the optimalpoint(if necessary): by the 5.1) | tr. Y,3_) Nots: Theremaybe extraboxsin lhe tablesabovglhal are notneeded.Loaveanv6xtraboxssblnk. Donotwritebelowthis line I to the 16 b6lo,vat lh minimum 10.120Polnbl Youa@giventhe assignmont conneot following nodesln th6 network two if lotal cost, Thecosl lo connect nodesis givenlhe netwoft belorv.Indicate 9n arc rvillb usdby gqglE if or that arc (seesample below). I will deductpointsif I can'ttell wilh cedainty an arc hasbonbolded if thereare straymarkson the network. Note: There may b multiple optimal answersas the cosls on lhe arcs have been randomlygenrated. Minimum Total Cost ..6 'tr,'' I 8 ... ,,, z Do not write below this line 10

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