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1、PROBLEMA:TheUltimateBrowniePanWhenbakinginarectangularpanheatisconcentratedinthe4cornersandtheproductgetsovercookedatthecorners(andtoalesserextentattheedges).Inaroundpantheheatisdistributedevenlyovertheentireouteredgeandtheproductisnotovercookedattheedges.However
2、,sincemostovensarerectangularinshapeusingroundpansisnotefficientwithrespecttousingthespaceinanoven.Developamodeltoshowthedistributionofheatacrosstheouteredgeofapanforpansofdifferentshapes-rectangulartocircularandothershapesinbetween.Assume1.AwidthtolengthratioofW
3、/Lfortheovenwhichisrectangularinshape.2.EachpanmusthaveanareaofA.3.Initiallytworacksintheoven,evenlyspaced.Developamodelthatcanbeusedtoselectthebesttypeofpan(shape)underthefollowingconditions:1.Maximizenumberofpansthatcanfitintheoven(N)2.Maximizeevendistributiono
4、fheat(H)forthepan3.Optimizeacombinationofconditions(1)and(2)whereweightspand(1-p)areassignedtoillustratehowtheresultsvarywithdifferentvaluesofW/Landp.InadditiontoyourMCMformattedsolution,prepareaonetotwopageadvertisingsheetforthenewBrownieGourmetMagazinehighlight
5、ingyourdesignandresults.PROBLEMB:Water,Water,EverywhereFreshwateristhelimitingconstraintfordevelopmentinmuchoftheworld.Buildamathematicalmodelfordetermininganeffective,feasible,andcost-efficientwaterstrategyfor2013tomeettheprojectedwaterneedsof[pickonecountryfrom
6、thelistbelow]in2025,andidentifythebestwaterstrategy.Inparticular,yourmathematicalmodelmustaddressstorageandmovement;de-salinization;andconservation.Ifpossible,useyourmodeltodiscusstheeconomic,physical,andenvironmentalimplicationsofyourstrategy.Provideanon-technic
7、alpositionpapertogovernmentalleadershipoutliningyourapproach,itsfeasibilityandcosts,andwhyitisthe“bestwaterstrategychoice.”Countries:UnitedStates,China,Russia,Egypt,orSaudiArabiaICMPROBLEMPROBLEMC:NetworkModelingofEarth'sHealthClickthetitlebelowtodownloadaPDFofth
8、e2013ICMProblem.YourICMsubmissionshouldconsistofa1pageSummarySheetandyoursolutioncannotexceed20pagesforamaximumof21pages.问题A：终极蛋糕锅当你使用一个方形的锅的时候，热量会聚集在四个角落并且角落的
