Expert Answer :MAT540 week 8 homework

Solved by a verified expert :MAT540Week8 HomeworkChapter41. BettyMalloy,owneroftheEagleTaverninPittsburgh,ispreparingforSuperBowlSunday,and shemustdeterminehowmuchbeertostock.Betty stocksthreebrandsofbeer-Yodel,Shotz,and Rainwater.The costpergallon (tothetavern owner)ofeach brand isasfollows:Brand Cost/GallonYodel $1.50Shotz 0.90Rainwater 0.50Thetavernhasabudgetof$2,000forbeerforSuperBowlSunday.BettysellsYodelatarateof$3.00pergallon,Shotzat$2.50pergallon,andRainwaterat$1.75pergallon.Basedonpast footballgames, Bettyhasdeterminedthemaximumcustomerdemandtobe400gallonsofYodel,500gallonsofshotz,and 300gallonsofRainwater. The tavernhas thecapacity tostock1,000 gallons ofbeer;Bettywants to stockup completely. Bettywants to determine thenumberofgallons ofeach brand ofbeerto ordersoasto maximize profit.a. Formulatealinearprogramming model for thisproblem. b. Solve the modelbyusingthe computer.2. Asresultofarecentlypassedbill,acongressman’sdistricthasbeenallocated$3millionfor programsandprojects.Itisup tothecongressmantodecide how to distributethemoney. The congressmanhasdecidetoallocate themoney tofourongoing programsbecauseof their importancetohisdistrict-ajobtrainingprogram,aparksproject,asanitationproject,anda mobilelibrary.However,thecongressmanwantsto distributethemoney inamannerthatwill pleasethemostvoters,or, inotherwords,gainhim themostvotesin theupcomingelection.His staff’sestimatesofthenumberofvotesgainedperdollarspent forthevarious programsareas follows.ProgramVotes/DollarJob training0.03Parks0.08Sanitation0.05Mobilelibrary0.03Inorderalsoto satisfyseverallocalinfluentialcitizenswhofinancedhiselection, heisobligated to observethefollowing guidelines:· None ofthe programs can receivemore than 30%of the totalallocation· Theamountallocatedtoparkscannotexceedthetotalallocatedtoboththesanitation projectandthe mobile library.· Theamountallocatedtojobtrainingmustatleastequaltheamountspentonthesanitation project.Anymoney notspentinthedistrictwillbereturnedtothegovernment;therefore,thecongressman wantstospenditall.Theecongressmanwantstoknowtheamounttoallocatetoeachprogram tomaximize his votes.a. Formulatea linearprogramming model for thisproblem. b. Solve the modelbyusingthe computer.3. AnnaBroderick is the dietician for the StateUniversity football team,andshe isattempting to determineanutritiouslunchmenufortheteam.Shehassetthefollowingnutritionalguidelines foreachlunch serving:· Between1,300 and 2,100 calories· At least4mgof iron· At least15 butno more than 55gof fat· At least30gofprotein· At least60gofcarbohydrates· No more than 35mgofcholesterolSheselectsthemenufromsevenbasicfooditems,asfollows,withthenutritionalcontributions perpound and the costas given:Calories(perlb.)Iron(mg/lb.)Protein(g/lb.)Carbo-hydrates(g/lb.)Fat(g/lb.)Cholesterol(mg/lb)Cost($/lb.)Chicken5004.2170301800.85Fish4803.18505903.35Ground beef8400.25820753502.45Driedbeans5903.21030300.85Lettuce400.460000.70Potatoes4502.251070000.45Milk(2%)2200.2162210200.82Thedieticianwantstoselectamenutomeetthenutritionalguidelineswhileminimizingthetotal costperserving.a. Formulatea linearprogramming model for thisproblemand solve.4. Dr. Maureen Becker, the head administrator at Jefferson County Regional Hospital, must determineaschedulefornursestomakesurethereareenoughofthemondutythroughoutthe day.Duringtheday,thedemandfornursesvaries. Maureenhasbrokenthedayintotwelve2- hourperiods.The slowesttimeoftheday encompassesthethreeperiods from12:00A.M. to6:00A.M.,whichbeginningatmidnight;requireaminimumof30,20,and40nurses,respectively. Thedemandfornursessteadilyincreasesduringthenextfourdaytimeperiods.Beginningwith the6:00A.M.-8:00A.M. period,aminimumof50,60,80,and80nursesarerequiredforthese fourperiods,respectively.After2:00P.M. thedemandfornursesdecreasesduring theafternoon andeveninghours.Forthefive2-hourperiodsbeginningat2:00P.M.andendingmidnight,70,70,60,50,and50nursesarerequired,respectively.Anursereportsforduty atthebeginning of oneof the2-hourperiods andworks8 consecutive hours (which is required in thenurses’ contract). Dr. Becker wants to determine a nursing schedule that will meet the hospital’s minimumrequirement throughout thedaywhile usingthe minimumnumberofnurses.a. Formulatea linearprogramming model for thisproblem.b. Solve the modelbyusingthe computer.5. Theproduction managerofVideotechnics Companyis attemptingto determinethe upcoming5-month production schedule forvideo recorders. Past productionrecords indicate that 2,000 recorders can beproduced permonth. An additional 600 recorders can beproduced monthlyonan overtime basis. Unit cost is $10 for recorders producedduringregularworkinghours and $15 forthose produced on an overtime basis. Contracted sales per month are as follows:MonthContracted Sales(units)1120022100324004300054000Inventorycarryingcostsare$2 per recorder per month. Themanager doesnot want any inventorycarried over past the fifth month. Themanagerwants to know themonthly production that willminimizetotal production and inventorycosts.a. Formulatealinear programmingmodel forthis problem. b. Solve the model byusingthe computer.