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1、3.2.1直线的点斜式方程若直线l经过点P1(x1,y1)，斜率为k,求直线l的方程.设点P(x,y)是直线l上不同于点P1的任意一点，则化简为——直线方程的点斜式3.2.1直线的点斜式此时直线的方程是x=x1当直线的倾斜角为0°时，当直线的倾斜角为90°时，直线没有斜率此时直线的方程是特殊直线例3.已知直线l在x轴上的截距比在y轴上的截距大1，且过定点(6,-2)，求直线l的方程.解：由已知可设直线l的方程为：令x=0,则直线l在y轴上的截距为令y=0,则直线l在x轴上的截距为由题意得即即或∴直线l的方程为：或即或例3.已知直线l在x轴
2、上的截距比在y轴上的截距大1，且过定点(6,-2)，求直线l的方程.解2：由已知可设直线l的方程为：令x=0,则直线l在y轴上的截距为：令y=0,则直线l在x轴上的截距为：由题意得解得∴直线l的方程为：或或TheNewsvendorModel报童模型“Toomuch”and“toolittle”costsCo=overagecostThecostoforderingonemoreunitthanwhatyouwouldhaveorderedhadyouknowndemand.Inotherwords,supposeyouhadleftov
3、erinventory(i.e.,youoverordered).Coistheincreaseinprofityouwouldhaveenjoyedhadyouorderedonefewerunit.Cu=underagecostThecostoforderingonefewerunitthanwhatyouwouldhaveorderedhadyouknowndemand.Inotherwords,supposeyouhadlostsales(i.e.,youunderordered).Cuistheincreaseinprofity
4、ouwouldhaveenjoyedhadyouorderedonemoreunit.BalancingtheriskandbenefitoforderingaunitOrderingonemoreunitincreasesthechanceofoverage…ExpectedlossontheQthunit=CoxF(Q)F(Q)=Distributionfunctionofdemand=Prob{Demand<=Q)…butthebenefit/gainoforderingonemoreunitisthereductioninthec
5、hanceofunderage:ExpectedgainontheQthunit=Cux(1-F(Q))Asmoreunitsareordered,theexpectedbenefitfromorderingoneunitdecreaseswhiletheexpectedlossoforderingonemoreunitincreases.NewsvendorexpectedprofitmaximizingorderquantityTomaximizeexpectedprofitorderQunitssothattheexpectedlo
6、ssontheQthunitequalstheexpectedgainontheQthunit:Rearrangetermsintheaboveequation->TheratioCu/(Co+Cu)iscalledthecriticalratio.（临界比或关键比例）Hence,tomaximizeprofit,chooseQsuchthatwedon’thavelostsales(i.e.,demandisQorlower)withaprobabilitythatequalsthecriticalratioTheNewsvendorM
7、odel: Performancemeasures绩效指标NewsvendormodelperformancemeasuresForanyorderquantitywewouldliketoevaluatethefollowingperformancemeasures:Expectedlostsales（期望销售损失）TheaveragenumberofunitsdemandexceedstheorderquantityExpectedsales（期望销售）(comparedtoexpecteddemand)Theaveragenumb
8、erofunitssold.Expectedleftoverinventory（期望售后剩余库存）Theaveragenumberofunitsleftoverattheendofthesea
