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1、运筹学题库带答案Chapter2Linearprogramming1.Afirmmanufactureschickenfeedbymixingthreedifferentingredients.Eachingredientcontainsthreekeynutrientsprotein,fatandvitamin.Theamountofeachnutrientcontainedin1kilogramofthethreebasicingredientsissummarizedinthefollowingtable:IngredientProtein(g
2、rams)Fat(grams)Vitamin(units)12511235245101603327190ThecostsperkilogramofIngredients1,2,and3are$0.55,$0.42and$0.38,respectively.Eachkilogramofthefeedmustcontainatleast35gramsofprotein,aminimumof8gramsoffatandamaximumof10gramsoffatandatleast200unitsofvitamins.Formulatealinearpro
3、grammingmodelforfindingthefeedmixthathastheminimumcostperkilogram.2.Forasupermarket,thefollowingclerksarerequired:DaysMin.numberofclerksMon20Tue16Wed13Thu16Fri19Sat14Sun12Eachclerkworks5consecutivedaysperweekandmaystartworkingonMonday,WednesdayorFriday.Theobjectiveistofindthesm
4、allestnumberofclerksrequiredtocomplywiththeaboverequirements.Formulatetheproblemasalinearprogrammingmodel.3.ConsiderthefollowingLPproblem:45(a)Sketchthefeasibleregion.(b)Findtwoalternativeoptimalextreme(corner)points.(c)Findaninfinitesetofoptimalsolutions.1.Apowerplanthasthreet
5、hermalgenerators.Thegenerators’generationcostsare$36/MW,$30/MW,and$25/MW,respectively.Theoutputlimitationforthegeneratorsisshowninthetable.Somemoment,thepowerdemandforthisplantis360MW,pleasesetupanLPoptimizationmodelandfindouttheoptimaloutputforeachgenerator(withlowestoperation
6、cost).GeneratorGenerationlowerlimitGenerationhigherlimit1502002501503501502.UsetheGraphicalSolutiontofindtheoptimalsolutionstothefollowingLP:45Solution：1.Letx1=theamountofIngredient1mixedin1kilogramofthechickenfeedx2=theamountofIngredient2mixedin1kilogramofthechickenfeedx3=thea
7、mountofIngredient3mixedin1kilogramofthechickenfeedTheLPmodelis:2.Letx1=numberofclerksstartworkingonMondayx2=numberofclerksstartworkingonWednesdayx3=numberofclerksstartworkingonFridayTheLPmodelis:451.(a)(b)Thetwoalternativeoptimalextremepointsare(4,3)and(6,3/2).(c)Theinfiniteset
8、ofoptimalsolutions:{λ(4,3)+(1−λ)(6,3/2):0≤λ≤12.Model:S
