Solve the question below using the attached excel templates with formulas for renting both slow and fast copies (labeled in the excel tabs).Question: The Decision Sciences Department is trying to determine whether to rent a slow or a fast copier. The department believes that an employee’s time is worth $15 per hour. The slow copier rents for $4 per hour, and it takes an employee an average of 10 minutes to complete copying. The fast copier rents for $15 per hour, and it takes an employee an average of six minutes to complete copying. On average, four employees per hour need to use the copying machine. (Assume the copying times and interarrival times to the copying machine are exponentially distributed.) Which machine should the department rent to minimize expected total cost per hour? HomefxInsertFunctionH322345678Renting a copierInputs (for slow system)Unit of timeArrival rateService rateOutputs9 Direct outputs from inputsMean time between arrivals272829303132331011 Mean time per service12 Traffic intensity1314 Summary measures15 Expected number in system16 Expected number in queue17 Expected time in system18 Expected time in queue363738Insert Draw3940414243Σ.V19 Percentage who don't wait in queue2021 Cost analysis22 Employee cost/hr23 Rental cost/hour2425 Waiting cost/hour26 Total Cost/hour444546474849505152535455A56AutoSum Recently Financial LogicalUsed57585960X ✔AReadyRetiremPlannin...jefxPage Layout?P12-10-Slow1/851/86=85/86V815/85-816/B51-812812/(1-812)-812^2/(1-B12)P12-10-FastBFormulasATexthourVunit&"s"unit&"s"customers/"&unitcustomers/"&unitunit&"s"-unit&"s"P13-32VDate &TimeCDataLookup &ReferenceP13-35VcustomerscustomersReviewVMath &TrigDNew Module 8 Problem Workbook (1)SolverTable for MacTell meView***VMoreFunctionsFNameManagerDistribution of number in system'n (customers)4Define NameUse in Formula ✓Create from Selection(1-$B$12) $B$12^E11FPin in system)GTrace PrecedentsTrace DependentsRemove Arrows ✓HDistribution of time in queue"t (in "&unit&"s)"27fxShowFormulasP(wait>t)$B$12*EXP(-$B$6*(1-$B$12) 2829303132333422 Employee cost/hr23 Rental cost/hour243536Home25 Waiting cost/hour26 Total Cost/hour2737338391 Renting a copier3 Inputs (for slow system)4Unit of time5 Arrival rate&Service rate7& Outputs40413fx Σ -InsertFunctionE19 Direct outputs from inputs10 Mean time between arrivals11 Mean time per service12 Traffic intensity1314 Summary measures15 Expected number in system16 Expected number in queue17 Expected time in system18 Expected time in queue19 Percentage who don't wait in queue2021 Cost analysis*434544454648InsertReadyRetiremlannin...jeBUDwwwDrawAutoSum Recently Financial LogicalUsedX VP12-10-SlowAfxPage Layout?P12-10-Fast●VAUG142=1/851/8685/86-815/85=816/B5-1-812P13-32FormulasAText=B12/(1-812)B12^2/(1-B12)VBDate &TimehourP13-35=unit&"s"unit&"s"="customers/"&unit="customers/"&unit=unit&"s"=unit&"s"Data ReviewLookup &ReferenceData+CWindow10Math &TrigVViewcustomerscustomers...HelpNew Module 8 Problem Workbook (1)SolverTable for MacTell meVMoreFunctionsDNameManager14Define Name vUse in Formula vCreate from SelectionDistribution of number in system="n (customers)"4AETrace PrecedentsVfxTrace DependentsFRemove Arrows Formulas Checking WindowShowWatchError=(1-$B$12) $B$12^E11WFP(n in system)See full Q&AEGHDistribution of time in queue="t (in "&unit&"s)"2P(wait>t)-$B$12 EXP(-SBS6*(1-$B$12) H11+CalculationOptions75%Shafce slowfor $15

From the given information, The department believes that the employees time is worth $15 per hour.…

zing a copier ats (for slow system) of time ce rate tputs rect outputs from Inputs man time between anivals can time per service affic intensity ummary measures expected number in system Expected number in queue Expected time in system Expected time in queue Percentage who don't wait in queue Cost analysis Employee cost/hr Rental cost/hour Waiting cost/hour Total Cost/hour D D 1 2 3 14 05 36 12 37 38 39 40 -1/85 -3/86 -85/86 812/1-812) 812-2/(1-812) -815/85 16/85 1-812 hour customers/"&unit customers/"&unit units "unit" C units" units customers customers D Distribution of number in system (customers) 4 9 1-$B$12) S8512 11 Pin in system) G H Distribution of time in queue et (in "&units "s" 2 P/wait > t $8512 EXPI-$B$61-58512)

zing a copier ats (for slow system) of time ce rate tputs rect outputs from Inputs man time between anivals can time per service affic intensity ummary measures expected number in system Expected number in queue Expected time in system Expected time in queue Percentage who don't wait in queue Cost analysis Employee cost/hr Rental cost/hour Waiting cost/hour Total Cost/hour D D 1 2 3 14 05 36 12 37 38 39 40 -1/85 -3/86 -85/86 812/1-812) 812-2/(1-812) -815/85 16/85 1-812 hour customers/"&unit customers/"&unit units "unit" C units" units customers customers D Distribution of number in system (customers) 4 9 1-$B$12) S8512 11 Pin in system) G H Distribution of time in queue et (in "&units "s" 2 P/wait > t $8512 EXPI-$B$61-58512)

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section12.5: Analytic Steady-state Queueing Models

Problem 11P

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