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1、2013ContestProblemsMCMPROBLEMSPROBLEMA:TheUltimateBrowniePanWhenbakinginarectangularpanheatisconcentratedinthe4cornersandtheproductgetsovercookedatthecorners(andtoalesserextentattheedges).Inaroundpantheheatisdistributedevenlyovertheentireouteredgeandtheproductisnotove
2、rcookedattheedges.However,sincemostovensarerectangularinshapeusingroundpansisnotefficientwithrespecttousingthespaceinanoven.Developamodeltoshowthedistributionofheatacrosstheouteredgeofapanforpansofdifferentshapes-rectangulartocircularandothershapesinbetween.Assume1.Aw
3、idthtolengthratioofW/Lfortheovenwhichisrectangularinshape.2.EachpanmusthaveanareaofA.3.Initiallytworacksintheoven,evenlyspaced.Developamodelthatcanbeusedtoselectthebesttypeofpan(shape)underthefollowingconditions:1.Maximizenumberofpansthatcanfitintheoven(N)2.Maximizeev
4、endistributionofheat(H)forthepan3.Optimizeacombinationofconditions(1)and(2)whereweightspand(1-p)areassignedtoillustratehowtheresultsvarywithdifferentvaluesofW/Landp.InadditiontoyourMCMformattedsolution,prepareaonetotwopageadvertisingsheetforthenewBrownieGourmetMagazin
5、ehighlightingyourdesignandresults. PROBLEMB:Water,Water,EverywhereFreshwateristhelimitingconstraintfordevelopmentinmuchoftheworld.Buildamathematicalmodelfordetermininganeffective,feasible,andcost-efficientwaterstrategyfor2013tomeettheprojectedwaterneedsof[pickonecount
6、ryfromthelistbelow]in2025,andidentifythebestwaterstrategy.Inparticular,yourmathematicalmodelmustaddressstorageandmovement;de-salinization;andconservation.Ifpossible,useyourmodeltodiscusstheeconomic,physical,andenvironmentalimplicationsofyourstrategy.Provideanon-techni
7、calpositionpapertogovernmentalleadershipoutliningyourapproach,itsfeasibilityandcosts,andwhyitisthe“bestwaterstrategychoice.”Countries:UnitedStates,China,Russia,Egypt,orSaudiArabia2013年赛题MCM问题问题A：终极布朗尼潘当在一个矩形的锅热烘烤时的4个角落中浓缩，并在拐角处（以及在较小程度上在边缘处）：产品会过头。在一个圆形盘的热量被均匀地分布在整个外缘
8、和在边缘处的产品不过头。然而，由于大多数烤炉是矩形的形状使用圆形平底锅是效率不高，相对于使用的空间的烘箱中。 开发一个模型来显示不同形状的平底锅锅的外边缘之间的热分布-矩形到圆形和在两者之间的其它形状。 假设 1。的宽度长度比W/L为烘箱是矩形的形
