OPTIMIZATION

Problem2:LinearProgramming(Optimization) InSeptember2020,25%ofthe cleaningjobswere2hourjobs,23%were2.5hourjobs,11.4%were3hourjobs,and11.4%were4hourjobs.Itcanbeseenfromthefilethatoneofthedecisionsthatneedtobemadeishowtoassigncleaningjobstoitsemployees.Althoughcurrentlythisdoesnotseemtobeachallengingdecision,thisdecisionwillbecomecrucialduringpeakseasons.Todemonstratehowlinearprogrammingcanhelpmakingthisdecision,wewillworkonahypotheticalscenario.Assumptionsmadebymeareshadedingray.

Supposethatthecompanywouldliketodecidehowtoassignjobstoworkersinaday.Let'sfocusonthe4majorjobtypes:2hourjobs,2.5hourjobs,3hourjobs,and4hourjobs.Assumethatthereare3workers:A,B,andC,withhourlywageof$10,$15,and$20,respectively.Supposethatonthenextday,thereare3,2,1,and1jobsofeachtype,respectively,andA,B,andCareabletoworkfor8,6,and4hours,respectively.

1Findtheassignmentplanforthenextdaythatcanminimizetotalcost(hint:youwillneedaconstraintthatrequireseachofyourdecisionvariablestobeaninteger)

2.Supposethatthenumbersofjobsrequiredare3,2,1,and2foreachtype,respectively.Explainhowthemodelcanbemodifiedandprovideyoursolution3

3.Discusshowthismodelcanbeexpandedorrevisedtoaccountforotherpotentialconsiderations.Forexample,theminimumworkinghoursrequiredbyeachemployee

4. Provideyourconclusionfromthisoptimizationtask

5. ProvideyoursuggestionstoCountyCleanersaboutthedatatheymayneedtocollecttoallowthisanalysis