第二次模拟赛赛题

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1、A:TheIrrigationProblemDesignalinearirrigationsystemtouniformlyspraywateronarectangularfieldiftheirrigationdevicemovesacrossthefieldataconstantrateinalinearfashionasshowninFigure1.Figure1LinearIrrigationSystem.Thelinearirrigationsystemconsistsofalongwaterpipe,generallysetonwheelsthatkeepitabovethe

2、leveloftheplants.Nozzlesareplacedperiodicallyalonethepipe,andeachsprayswaterinacircularregion.Theentiresystemmovesslowlydownthefield,wateringtheplantsbeneathasitmoves.Youhave100feetofpipeand20nozzlesavailable.Youhaveenoughpumpstokeepupthepressureoneachofthenozzlessotheydeliverauniformspraytoacirc

3、ularregion50feetinradius.Howfarapartshouldthenozzlesbeplacedtoproducethemostuniformdistributionofwateronafield1000feetwide?B:PredictingPumpkinWeights Atypicalcontestinthefallistoguesstheweightofapumpkinwithoutascale.Usingjustafewmeasurements,canyoupredicttheweightofapumpkin?Yourassignmentistowrit

4、eapaperthatusesthemodelingprocesstoanswerthisquestion.First,youwillwanttodiscussvariablesandassumptionssuchasgeometricsimilarity.Youwillalsohavetouseoneormore(length)measurementstoestimateweight.Ifyouhaveaccesstosomepumpkins,youmaywishtodecidewhichvariablesareimportantandtakeyourownmeasurements.I

5、fnot,youmayusethedatafoundbelow.Afteryouhaveyourdata,solve/verifythemodel.Youmaywanttousemorethanonetechnique,usingoneormoremeasurements.Whichmodeldidyoufeelwasthe"best"?Howaccurateisyourmodel?Discussthebalancebetweenaccuracyandsimplicity.Howwillmeasurementerroraffectyourpredict

6、ions?Overall,whatmodeldoyouchoosetopredictapumpkin'sweightandwhy?Whataboutimplementation?Ifyou'rejusttryingtopredictonepumpkin'sweight,thenacomplicatedformulamightbeokay.However,supposeanorganizationissellingpumpkinstothegeneralpublicandwantstobaseitspricesonweight.Ifas

7、caleisunavailable,thenhowwouldyousuggesttheyimplementyourmodel?Ifavailable,testyourmodelonsomenewpumpkins.Discussyourconclusions. 2003Data       circumferences    heighthoriz.vertical1vertical2 weight 422.819.319.2 0.25 630.426.426.5 0.6 7.531.