2013年美国大学生数学建模竞赛试题.doc

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1、2013ContestProblemsMCMPROBLEMSPROBLEMA: TheUltimateBrowniePanWhenbakinginarectangularpanheatisconcentratedinthe4cornersandtheproductgetsovercookedatthecorners(andtoalesserextentattheedges).Inaroundpantheheatisdistributedevenlyovertheentireouteredgeandthep

2、roductisnotovercookedattheedges.However,sincemostovensarerectangularinshapeusingroundpansisnotefficientwithrespecttousingthespaceinanoven.Developamodeltoshowthedistributionofheatacrosstheouteredgeofapanforpansofdifferentshapes-rectangulartocircularandothe

3、rshapesinbetween.Assume1.Awidthtolengthratioof W/L fortheovenwhichisrectangularinshape.2.Eachpanmusthaveanareaof A.3.Initiallytworacksintheoven,evenlyspaced. Developamodelthatcanbeusedtoselectthebesttypeofpan(shape)underthefollowingconditions:1.Maximizenu

4、mberofpansthatcanfitintheoven(N)2.Maximizeevendistributionofheat(H)forthepan 3.Optimizeacombinationofconditions(1)and(2)whereweightspand(1- p)areassignedtoillustratehowtheresultsvarywithdifferentvaluesof W/L and p. InadditiontoyourMCMformattedsolution,pre

5、pareaonetotwopageadvertisingsheetforthenewBrownieGourmetMagazinehighlightingyourdesignandresults. PROBLEMB: Water,Water,EverywhereFreshwateristhelimitingconstraintfordevelopmentinmuchoftheworld.Buildamathematicalmodelfordetermininganeffective,feasible,and

6、cost-efficientwaterstrategyfor2013tomeettheprojectedwaterneedsof[pickonecountryfromthelistbelow]in2025,andidentifythebestwaterstrategy.Inparticular,yourmathematicalmodelmustaddressstorageandmovement;de-salinization;andconservation.Ifpossible,useyourmodelt

7、odiscusstheeconomic,physical,andenvironmentalimplicationsofyourstrategy.Provideanon-technicalpositionpapertogovernmentalleadershipoutliningyourapproach,itsfeasibilityandcosts,andwhyitisthe“bestwaterstrategychoice.” Countries:UnitedStates,China,Russia,Egyp

8、t,orSaudiArabia