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1、TeamControlNumberForofficeuseonlyT1T2T3T418674ProblemChosenForofficeuseonlyF1F2F3F42013MathematicalContestinModeling(MCM)SummarySheet(Attachacopyofthispagetoyoursolutionpaper.)Typeasummaryofyourresultsonthispage・Donotineludethenameofyourschool,advisor,orteammembersonthispage・summa
2、ryOursolutionpapermainlydealswiththefollowingproblems:•Howtomeasurethedistributionofheatacrosstheouteredgeofpansindifferentshapesandmaximizeevendistributionofheatforthepan•Howtodesigntheshapeofpansinordertomakethebestofspaceinanoven•Howtooptimizeacombinationoftheformertwocondition
3、s・Whenbuildingthemathematicmodels,wemakesomeassumptionstogetthemtobemorereasonable.Oneofthemajorassumptionsisthatheatisevenlydistributedwithintheoven.Wealsointroducesomenewvariablestohelpdescribetheproblem・Tosolvealloftheproblems,wedesignthreemodels・Basedontheequationofheatconduct
4、ion,wcsimulatethedistributionofheatacrosstheouteredgewiththehelpofsomemathematicalsoftwares.Inaddition,takingthesameareaofallthepansintoconsideration,weanalyzetherateofspaceutilizationratioinsteadofthinkingaboutmaximalnumberofpanscontainedintheoven.What，smore,weoptimizeacombinatio
5、nofconditions(1)and(2)tofindoutthebestshapeandbuildafunctiontoshowtherelationbetweenthewcightincssofbothconditionsandthewidthtolengthratio,andtoillustratehowtheresultsvarywithdifferentvaluesofW/Landp.Totestourmodels,wecomparetheresultsobtainedbystimulationandourmodels,tofindthatou
6、rmodelsfitthetruthwell.Yet,therearestillsmallerrors.Forinstance,inModelOne,theerroriswithin1.2%.Inourmodels,wcintroducetherateofsatisfactiontoshowhoweventhedistributionofheatacrosstheouteredgeofapanisclearly.AndwiththehelpofmathematicalsoftwaressuchasMatlab,weaddmanypicturesintoou
7、rmodels,makingthemmoreintuitivelyclea匚Butourmodelsarenotperfectandtherearesomeshortcomingssuchaslackingspecificanalysisofthedistributionofheatacrosstheouteredgeofapanofirregularshapes.Inspiteofthese,ourmodelscanmainlypredicttheactualconditions,withinreasonablerangeoferror.TheUltim
8、ateBrowniePanAbstractWeintroducet
