美国数学建模竞赛1985试题.docx
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美国数学建模竞赛1985试题.docx
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美国数学建模竞赛1985试题
1985~2014年美国大学生数学建模竞赛题目集锦
目录
1985MCMA:
AnimalPopulations3
1985MCMB:
StrategicReserveManagement3
1986MCMA:
HydrographicData4
1986MCMB:
Emergency-FacilitiesLocation4
1987MCMA:
TheSaltStorageProblem5
1987MCMB:
ParkingLotDesign5
1988MCMA:
TheDrugRunnerProblem5
1988MCMB:
PackingRailroadFlatcars6
1989MCMA:
TheMidgeClassificationProblem6
1989MCMB:
AircraftQueueing6
1990MCMA:
TheBrain-DrugProblem6
1990MCMB:
SnowplowRouting7
1991MCMA:
WaterTankFlow8
1991MCMB:
TheSteinerTreeProblem8
1992MCMA:
Air-Traffic-ControlRadarPower8
1992MCMB:
EmergencyPowerRestoration9
1993MCMA:
OptimalComposting10
1993MCMB:
Coal-TippleOperations11
1994MCMA:
ConcreteSlabFloors11
1994MCMB:
NetworkDesign12
1995MCMA:
HelixConstruction13
1995MCMB:
FacultyCompensation13
1996MCMA:
SubmarineTracking13
1996MCMB:
PaperJudging13
1997MCMA:
TheVelociraptorProblem14
1997MCMB:
MixWellforFruitfulDiscussions15
1998MCMA:
MRIScanners16
1998MCMB:
GradeInflation17
1999MCMA:
DeepImpact17
1999MCMB:
UnlawfulAssembly18
2000MCMA:
AirTrafficControl18
2000MCMB:
RadioChannelAssignments19
2001MCMA:
ChoosingaBicycleWheel20
2001MCMB:
EscapingaHurricane'sWrath(AnIllWind...)21
2002MCMA:
WindandWaterspray23
2002MCMB:
AirlineOverbooking23
2003MCMA:
TheStuntPerson24
2003MCMB:
GammaKnifeTreatmentPlanning24
2004MCMA:
AreFingerprintsUnique?
25
2004MCMB:
AFasterQuickPassSystem25
2005MCMA:
FloodPlanning26
2005MCMB:
Tollbooths26
2006MCMA:
PositioningandMovingSprinklerSystemsforIrrigation27
2006MCMB:
WheelChairAccessatAirports27
2007MCMA:
Gerrymandering29
2007MCMB:
TheAirplaneSeatingProblem29
2008MCMA:
TakeaBath30
2008MCMB:
CreatingSudokuPuzzles30
2009MCMA:
DesigningaTrafficCircle30
2009MCMB:
EnergyandtheCellPhone30
2010MCMA:
TheSweetSpot32
2010MCMB:
Criminology32
2011MCMA:
SnowboardCourse33
2011MCMB:
RepeaterCoordination33
2012MCMA:
TheLeavesofaTree33
2012MCMB:
CampingalongtheBigLongRiver34
2013MCMA:
TheUltimateBrowniePan34
2013MCMB:
Water,Water,Everywhere35
2014MCMA:
TheKeep-Right-Except-To-PassRule35
2014MCMB:
CollegeCoachingLegends36
1985MCMA:
AnimalPopulations
Chooseafishormammalforwhichappropriatedataareavailabletomodelitaccurately.Modeltheanimal'snaturalinteractionswithitsenvironmentbyexpressingpopulationlevelsofdifferentgroupsintermsofthesignificantparametersoftheenvironment.Thenadjustthemodeltoaccountforharvestinginaformconsistentwiththeactualmethodbywhichtheanimalisharvested.Includeanyoutsideconstraintsimposedbyfoodorspacelimitationsthataresupportedbythedata.
Considerthevalueofthevariousquantitiesinvolved,thenumberharvested,andthepopulationsizeitself,inordertodeviseanumericalquantitythatrepresentstheoverallvalueoftheharvest.Findaharvestingpolicyintermsofpopulationsizeandtimethatoptimizesthevalueoftheharvestoveralongperiodoftime.Checkthatthepolicyoptimizesthatvalueoverarealisticrangeofenvironmentalconditions.
1985MCMB:
StrategicReserveManagement
Cobalt,whichisnotproducedintheUS,isessentialtoanumberofindustries.(Defenseaccountedfor17%ofthecobaltproductionin1979.)MostcobaltcomesfromcentralAfrica,apoliticallyunstableregion.TheStrategicandCriticalMaterialsStockpilingActof1946requiresacobaltreservethatwillcarrytheUSthroughathree-yearwar.Thegovernmentbuiltupastockpileinthe1950s,soldmostofitoffintheearly1970s,andthendecidedtobuilditupagaininthelate1970s,withastockpilegoalof85.4millionpounds.Abouthalfofthisstockpilehadbeenacquiredby1982.
Buildamathematicalmodelformanagingastockpileofthestrategicmetalcobalt.Youwillneedtoconsidersuchquestionsas:
▪Howbigshouldthestockpilebe?
▪Atwhatrateshoulditbeacquired?
▪Whatisareasonablepricetopayforthemetal?
Youwillalsowanttoconsidersuchquestionsas:
▪Atwhatpointshouldthestockpilebedrawndown?
▪Atwhatrateshoulditbedrawndown?
▪Atwhatpriceisitreasonabletosellthemetal?
▪Howshoulditbeallocated?
UsefulInformationonCobalt
Thegovernmenthasprojectedaneedot25millionpoundsofcobaltin1985.
TheU.S.hasabout100millionpoundsofprovencobaltdeposits.Productionbecomeseconomicallyfeasiblewhenthepricereaches$22/lb(asoccurredin1981).Ittakesfouryearstogetoperationsrolling,andthsnsixmillionpoundsperyearcanbeproduced.
In1980,1.2millionpoundsofcobaltwererecycled,7%oftotalconsumption.
1986MCMA:
HydrographicData
ThetablebelowgivesthedepthZofwaterinfeetforsurfacepointswithr
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