BUS 660 Topic 8 Final Exam (April Term)

1. Question:Acompanymakestwoproductsfromsteel; onerequires 2tonsofsteelandtheotherrequires3tons.Thereare100tonsofsteelavailabledaily.Aconstraintondaily production could bewrittenas:2x1+3x2≤100. 2. Question:Letx1,x2,andx3be0-1variableswhosevaluesindicatewhethertheprojectsarenotdone(0)oraredone(1).Whichanswerbelowindicatesthatatleasttwooftheprojectsmust bedone? 3. Question:The constraintx1 +x2+x3 +x4 ≤2 meansthattwooutofthefirstfourprojectsmust be selected. 4. Question:EachpointontheefficientfrontiergraphassociatedwiththeMarkowitzportfoliomodelisthe 5. Question:Consideramaximalflowprobleminwhichvehicletrafficenteringacityisroutedamongseveralroutesbeforeeventuallyleavingthecity.Whenrepresented withanetwork, 6. Question:AssumingW1,W2andW3are0-1integervariables,theconstraintW1+W2+W31isoftencalleda 7. Question:LetM bethenumber of unitstomakeandBbe thenumberofunits tobuy. Ifitcosts$2tomakeaunitand$3tobuyaunitand4000 unitsare needed,theobjectivefunctionis 8. Question:Thedualpricefor aconstraintthatcomparesfundsusedwithfundsavailableis.058.Thismeansthat 9. Question:Problem 9-11(Algorithmic): Edwards Manufacturing Company purchases two component parts from three different suppliers. The suppliershave limited capacity, and no one supplier can meet all the company’s needs. In addition, the suppliers chargedifferentpricesforthecomponents.Componentpricedata(inpriceperunit)areasfollows: Each supplier has a limited capacity in terms of the total number of components it can supply.However,aslongasEdwardsprovidessufficientadvanceorders,eachsuppliercandevoteitscapacityto component1, component2,orany combinationofthetwocomponents,ifthe total numberof unitsorderediswithinitscapacity.Suppliercapacitiesareasfollows: IftheEdwardsproductionplanforthenextperiodincludes1025unitsofcomponent1and825unitsof component2,whatpurchasesdoyourecommend?Thatis,howmanyunitsofeachcomponentshouldbeorderedfromeachsupplier? 10. Question:Todevelopaportfoliothatprovidesthebestreturnpossiblewithaminimumrisk,thelinearprogrammingmodelwill haveanobjectivefunctionwhich 11. Question:ThetotalcostforawaitinglinedoesNOTspecificallydependon 12. Question:Themediaselectionmodelpresentedinthetextbookinvolvesmaximizingthenumberofpotentialcustomersreachedsubjecttoaminimumtotalexposure qualityrating. 13. Question:LetPij=theproductionofproductiinperiodj.Tospecifythatproductionofproduct1inperiod3andinperiod4differsby nomore than 100units, 14. Question:Thenumberofunitsshippedfromoriginitodestinationjisrepresentedby 15. Question:Problem 15-09 (Algorithmic) Mart’s barber shop has one barber. Customers have an arrival of 2.2 customers per hour,…… 16. Question:TheassumptionthatarrivalsfollowaPoissonprobabilitydistributionisequivalenttotheassumptionthatthetimebetweenarrivalshas 17. Question:IfarrivalsoccuraccordingtothePoissondistributionevery20minutes,thenwhichisNOTtrue? 18. Question:Theoverallgoalofportfoliomodelsistocreateaportfoliothatprovidesthebestbalancebetween 19. Question:Ifatransportationproblemhasfouroriginsandfivedestinations,theLPformulationoftheproblemwillhave 20. Question:Formanywaitinglinesituations,thearrivalsoccurrandomlyandindependentlyofotherarrivalsandithasbeenfoundthatagood descriptionofthearrivalpattern is providedby 21. Question:Modernrevenuemanagementsystemsmaximizerevenuepotentialforanorganizationbyhelpingtomanage 22. Question:Problem12-27(Algorithmic): AndalusFurnitureCompanyhastwomanufacturingplants,oneatAynorandanotheratSpartanburg.Thecostindollarsofproducingakitchenchair ateachofthetwoplantsisgivenhere. Aynor:Cost=66Q1+6Q12+105 Spartanburg:Cost=20Q2+2.5Q22+156 Where Q1 = number of chairs produced at AynorQ2= number of chairs produced atSpartanburg Andalusneedstomanufactureatotalof50kitchenchairstomeetanorderjustreceived.HowmanychairsshouldbemadeatAynorandhowmanyshouldbemadeatSpartanburginordertominimizetotalproductioncost?Whenrequired,roundyouranswerstothenearestdollar. 23. Question:Theassignmentproblemconstraintx31+x32+x33+x34≤2means 24. Question:ThesolutiontotheLPRelaxationofamaximizationintegerlinearprogramprovides 25. Question:Problem10-09(Algorithmic): TheAceManufacturingCompanyhasordersforthreesimilarproducts:Threemachinesare availableforthe manufacturingoperations. Allthreemachinescanproducealltheproductsatthesameproductionrate.However,duetovaryingdefectpercentagesofeachproductoneachmachine,theunitcostsoftheproductsvarydependingonthemachineused.Machinecapacitiesforthenextweekandtheunitcostsareasfollows:Usethetransportationmodeltodeveloptheminimumcostproductionschedulefortheproductsandmachines.Showthelinear programmingformulation.Ifrequired,roundyouranswerstoonedecimalplace.Thelinearprogrammingformulationandoptimalsolutionareshown. 26. Question:Iftheacceptance ofprojectAis conditionalontheacceptanceof project B,andviceversa,theappropriateconstraint to use isa 27. Question:Problem 11-9(Algorithmic): Hawkins Manufacturing Company produces connecting rods for 4- and 6-cylinder automobile enginesusing the same production line. The cost required to set up the production line to produce the 4-cylinderconnectingrodsis$2200,andthecostrequiredtosetuptheproductionlineforthe6-cylinderconnectingrodsis $3700. Manufacturing costs are $16 for each 4-cylinder connecting rod and $18 for each 6-cylinderconnectingrod.Hawkins makesa decisionattheendofeachweekastowhichproductwillbemanufacturedthe following week. If there is a production changeover from one week to the next, the weekend is used toreconfigurethe productionline. Once the linehasbeensetup, the weekly productioncapacitiesare 5900 6-cylinderconnectingrodsand85004-cylinderconnectingrods. Let x4=thenumberof4-cylinderconnectingrodsproducednextweek x6=thenumberof6-cylinderconnectingrodsproducednextweek s4=1iftheproductionlineissetuptoproducethe4-cylinderconnectingrods;0ifotherwise s6=1iftheproductionlineissetuptoproducethe6-cylinderconnectingrods;0ifotherwise Usingthedecisionvariablesx4ands4,writeaconstraintthatlimitsnextweek'sproductionofthe4-cylinderconnectingrodstoeither0or8500units. Usingthedecisionvariablesx6ands6,writeaconstraintthatlimitsnextweek'sproductionofthe6-cylinderconnectingrodstoeither0or5900units. 28. Question:Problem9-15: Bay Oil produces two types of fuels (regular and super) by mixing three ingredients. The majordistinguishing feature of the two products is the octane level required. Regular fuel must have aminimumoctanelevelof90 whilesupermusthave alevelofatleast100.Thecostperbarrel,octanelevels,andavailableamounts(in barrels)for theupcomingtwo-weekperiodareshown inthefollowingtable.Likewise,themaximumdemandforeachendproductandtherevenuegeneratedperbarrelareshown. Developandsolvealinearprogrammingmodeltomaximizecontributiontoprofit.LetRi=thenumberofbarrelsofinputitousetoproduceRegular,i=1,2,3 Si=thenumberofbarrelsofinputitousetoproduceSuper,i=1,2,3 Ifrequired,roundyouranswerstoonedecimalplace.Forsubtractiveornegativenumbersuseaminussignevenifthereisa+signbeforetheblank. (Example:-300) 29. Question:Problem 15-7(Algorithmic): Speedy Oil provides a single-server automobile oil change and lubrication service. Customers provide anarrival rate of 3.5 cars per hour. The service rate is 5 cars per hour. Assume that arrivals follow a Poissonprobabilitydistributionandthatservicetimesfollowanexponentialprobabilitydistribution. 30. Question:Inawaitinglinesituation,arrivalsoccur,onaverage,every10minutes,and10unitscanbereceivedeveryhour.Whatareλandμ?