2002美国数学建模数学竞赛试题及翻译

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1、2002MCMA:WindandWatersprayAnornamentalfountain（喷泉）inalargeopenplaza（广场）surroundedbybuildingssquirts（喷水池）waterhighintotheair.Ongustydays,thewindblowssprayfromthefountainontopassersby.Thewater-flowfromthefountainiscontrolledbyamechanismlinkedtoananemometer(whichmeasureswindspeedanddirection)locat

2、edontopofanadjacentbuilding.Theobjectiveofthiscontrolistoprovidepassersbywithanacceptablebalancebetweenanattractivespectacleandasoaking:Theharderthewindblows,thelowerthewatervolumeandheighttowhichthewaterissquirted,hencethelesssprayfallsoutsidethepoolarea.Yourtaskistodeviseanalgorithm（算法）whichu

3、sesdataprovidedbytheanemometertoadjustthewater-flowfromthefountainasthewindconditionschange.风和喷水池在一个露天广场里装饰喷泉把水喷到控制，当有风吹过时，水滴飘向行人。喷泉射出的水流是由一个与风速计（用于测量风的速度和方向）项链的机械装置控制的，风速计安装在一幢邻近楼房顶上。这个控制的实际作用是要为行人在赏心悦目的景象和淋水浸湿之间提供可以接受的平衡点：风刮的越猛，水量和喷射的高度就越低，从而较少的水花落在水池范围以外。你的任务是设计一个算法，随着风力条件的变化，运用风速计给出的数据来调整由喷

4、泉射出的水流。2002MCMB:AirlineOverbookingYou'reallpackedandreadytogoonatriptovisityourbestfriendinNewYorkCity.Afteryoucheckinattheticketcounter,theairlineclerkannouncesthatyourflighthasbeenoverbooked.Passengersneedtocheckinimmediatelytodetermineiftheystillhaveaseat.Historically,airlinesknowthatonlyace

5、rtainpercentageofpassengerswhohavemadereservationsonaparticularflightwillactuallytakethatflight.Consequently,mostairlinesoverbook-thatis,theytakemorereservationsthanthecapacityoftheaircraft.Occasionally,morepassengerswillwanttotakeaflightthanthecapacityoftheplaneleadingtooneormorepassengersbein

6、gbumpedandthusunabletotaketheflightforwhichtheyhadreservations.Airlinesdealwithbumpedpassengersinvariousways.Somearegivennothing,somearebookedonlaterflightsonotherairlines,andsomearegivensomekindofcashorairlineticketincentive.Considertheoverbookingissueinlightofthecurrentsituation:Lessflightsby

7、airlinesfrompointAtopointBheightenedsecurityatandaroundairportsPassengers'fearLossofbillionsofdollarsinrevenuebyairlinestodate.Buildamathematicalmodelthatexaminestheeffectsthatdifferentoverbookingschemeshaveontherevenuereceivedbya