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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
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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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? 

Home fx Insert Function H32 2 3 4 5 6 7 8 Renting a copier Inputs (for slow system) Unit of time Arrival rate Service rate Outputs 9 Direct outputs from inputs Mean time between arrivals 27 28 29 30 31 32 33 10 11 Mean time per service 12 Traffic intensity 13 14 Summary measures 15 Expected number in system 16 Expected number in queue 17 Expected time in system 18 Expected time in queue 36 37 38 Insert Draw 39 40 41 42 43 Σ. V 19 Percentage who don't wait in queue 20 21 Cost analysis 22 Employee cost/hr 23 Rental cost/hour 24 25 Waiting cost/hour 26 Total Cost/hour 44 45 46 47 48 49 50 51 52 53 54 55 A 56 AutoSum Recently Financial Logical Used 57 58 59 60 X ✔ A Ready Retirem Plannin...je fx Page Layout ? P12-10-Slow 1/85 1/86 =85/86 V 815/85 -816/B5 1-812 812/(1-812) -812^2/(1-B12) P12-10-Fast B Formulas A Text hour V unit&"s" unit&"s" customers/"&unit customers/"&unit unit&"s" -unit&"s" P13-32 V Date & Time C Data Lookup & Reference P13-35 V customers customers Review V Math & Trig D New Module 8 Problem Workbook (1) SolverTable for Mac Tell me View *** V More Functions F Name Manager Distribution of number in system 'n (customers) 4 Define Name Use in Formula ✓ Create from Selection (1-$B$12) $B$12^E11 F Pin in system) G Trace Precedents Trace Dependents Remove Arrows ✓ H Distribution of time in queue "t (in "&unit&"s)" 2 7fx Show Formulas P(wait>t) $B$12*EXP(-$B$6*(1-$B$12)
Transcribed Image Text:Home fx Insert Function H32 2 3 4 5 6 7 8 Renting a copier Inputs (for slow system) Unit of time Arrival rate Service rate Outputs 9 Direct outputs from inputs Mean time between arrivals 27 28 29 30 31 32 33 10 11 Mean time per service 12 Traffic intensity 13 14 Summary measures 15 Expected number in system 16 Expected number in queue 17 Expected time in system 18 Expected time in queue 36 37 38 Insert Draw 39 40 41 42 43 Σ. V 19 Percentage who don't wait in queue 20 21 Cost analysis 22 Employee cost/hr 23 Rental cost/hour 24 25 Waiting cost/hour 26 Total Cost/hour 44 45 46 47 48 49 50 51 52 53 54 55 A 56 AutoSum Recently Financial Logical Used 57 58 59 60 X ✔ A Ready Retirem Plannin...je fx Page Layout ? P12-10-Slow 1/85 1/86 =85/86 V 815/85 -816/B5 1-812 812/(1-812) -812^2/(1-B12) P12-10-Fast B Formulas A Text hour V unit&"s" unit&"s" customers/"&unit customers/"&unit unit&"s" -unit&"s" P13-32 V Date & Time C Data Lookup & Reference P13-35 V customers customers Review V Math & Trig D New Module 8 Problem Workbook (1) SolverTable for Mac Tell me View *** V More Functions F Name Manager Distribution of number in system 'n (customers) 4 Define Name Use in Formula ✓ Create from Selection (1-$B$12) $B$12^E11 F Pin in system) G Trace Precedents Trace Dependents Remove Arrows ✓ H Distribution of time in queue "t (in "&unit&"s)" 2 7fx Show Formulas P(wait>t) $B$12*EXP(-$B$6*(1-$B$12)
28 29 30 31 32 33 34 22 Employee cost/hr 23 Rental cost/hour 24 35 36 Home 25 Waiting cost/hour 26 Total Cost/hour 27 37 338 39 1 Renting a copier 3 Inputs (for slow system) 4 Unit of time 5 Arrival rate & Service rate 7 & Outputs 40 41 3 fx Σ - Insert Function E1 9 Direct outputs from inputs 10 Mean time between arrivals 11 Mean time per service 12 Traffic intensity 13 14 Summary measures 15 Expected number in system 16 Expected number in queue 17 Expected time in system 18 Expected time in queue 19 Percentage who don't wait in queue 20 21 Cost analysis * 43 45 44 45 46 48 Insert Ready Retirem lannin...je BUD www Draw AutoSum Recently Financial Logical Used X V P12-10-Slow A fx Page Layout ? P12-10-Fast ● V AUG 14 2 =1/85 1/86 85/86 -815/85 =816/B5 -1-812 P13-32 Formulas A Text =B12/(1-812) B12^2/(1-B12) V B Date & Time hour P13-35 =unit&"s" unit&"s" ="customers/"&unit ="customers/"&unit =unit&"s" =unit&"s" Data Review Lookup & Reference Data + C Window 10 Math & Trig V View customers customers ... Help New Module 8 Problem Workbook (1) SolverTable for Mac Tell me V More Functions D Name Manager 14 Define Name v Use in Formula v Create from Selection Distribution of number in system ="n (customers)" 4 A E Trace Precedents Vfx Trace Dependents FRemove Arrows Formulas Checking Window Show Watch Error =(1-$B$12) $B$12^E11 W F P(n in system) See full Q&A E G H Distribution of time in queue ="t (in "&unit&"s)" 2 P(wait>t) -$B$12 EXP(-SBS6*(1-$B$12) H11 + Calculation Options 75% Sha fc e slow for $15
Transcribed Image Text:28 29 30 31 32 33 34 22 Employee cost/hr 23 Rental cost/hour 24 35 36 Home 25 Waiting cost/hour 26 Total Cost/hour 27 37 338 39 1 Renting a copier 3 Inputs (for slow system) 4 Unit of time 5 Arrival rate & Service rate 7 & Outputs 40 41 3 fx Σ - Insert Function E1 9 Direct outputs from inputs 10 Mean time between arrivals 11 Mean time per service 12 Traffic intensity 13 14 Summary measures 15 Expected number in system 16 Expected number in queue 17 Expected time in system 18 Expected time in queue 19 Percentage who don't wait in queue 20 21 Cost analysis * 43 45 44 45 46 48 Insert Ready Retirem lannin...je BUD www Draw AutoSum Recently Financial Logical Used X V P12-10-Slow A fx Page Layout ? P12-10-Fast ● V AUG 14 2 =1/85 1/86 85/86 -815/85 =816/B5 -1-812 P13-32 Formulas A Text =B12/(1-812) B12^2/(1-B12) V B Date & Time hour P13-35 =unit&"s" unit&"s" ="customers/"&unit ="customers/"&unit =unit&"s" =unit&"s" Data Review Lookup & Reference Data + C Window 10 Math & Trig V View customers customers ... Help New Module 8 Problem Workbook (1) SolverTable for Mac Tell me V More Functions D Name Manager 14 Define Name v Use in Formula v Create from Selection Distribution of number in system ="n (customers)" 4 A E Trace Precedents Vfx Trace Dependents FRemove Arrows Formulas Checking Window Show Watch Error =(1-$B$12) $B$12^E11 W F P(n in system) See full Q&A E G H Distribution of time in queue ="t (in "&unit&"s)" 2 P(wait>t) -$B$12 EXP(-SBS6*(1-$B$12) H11 + Calculation Options 75% Sha fc e slow for $15
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