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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?

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?

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?

fx Insert Function H31 5 1 Renting a copier 2 3 Inputs (for slow system) 4 Unit of time Arrival rate Service rate 21 Cost analysis 22 Employee cost/hr 23 Rental cost/hour 24 6 7 & Outputs 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 25 Waiting cost/hour 26 Total Cost/hour 27 28 29 30 31 32 Page Layout Σ.. ? AutoSum Recently Financial Logical Used 34 35 36 37 38 39 41 42 43 44 45 46 47 48 x ✓ fx ▶ Ready A P12-10-Slow 0 P12-10-Fast AUG 16 1 2 Formulas A Text =1/85 =1/B6 =B5/B6 15 15 =812/(1-812) -812^2/(1-812) =815/85 =B16/85 =1-B12 -822 111 -825 111 B P13-32 Date & Time hour Data v Lookup & Reference ="customers/"&unit ="customers/"&unit unit&"s" =unit&"s" =unit&"s" =unit&"s" Review Summary Output Ө C V Math & Trig View More Functions customers customers P13-35 + D M08_qa_Colbert SolverTable for Mac Name Manager MacBook Pro Define Name v Use in Formula v Create from Selection E Distribution of number in system ="n (customers)" 4 Tell me =(1-$B$12) $B$12^E11 MAT Trace Precedents Trace Dependents Remove Arrows ✓ F P(n in system) 160 Show Error Watch Formulas Checking Window G H Distribution of time in queue ="t (in "&unit&"s)" 2 E Share Calculation Calculate Options + 75% Calculate -$B$12*EXP(-$B$6 (1-$B$12) H11) P(wait>t)
Transcribed Image Text:fx Insert Function H31 5 1 Renting a copier 2 3 Inputs (for slow system) 4 Unit of time Arrival rate Service rate 21 Cost analysis 22 Employee cost/hr 23 Rental cost/hour 24 6 7 & Outputs 9 Direct outputs from inputs 10 Mean time between arrivals 11 Mean time per service 12 Traffic intensity 13 14 Summary measures 15 Expected number in system 16 Expected number in queue 17 Expected time in system 18 Expected time in queue 19 Percentage who don't wait in queue 20 25 Waiting cost/hour 26 Total Cost/hour 27 28 29 30 31 32 Page Layout Σ.. ? AutoSum Recently Financial Logical Used 34 35 36 37 38 39 41 42 43 44 45 46 47 48 x ✓ fx ▶ Ready A P12-10-Slow 0 P12-10-Fast AUG 16 1 2 Formulas A Text =1/85 =1/B6 =B5/B6 15 15 =812/(1-812) -812^2/(1-812) =815/85 =B16/85 =1-B12 -822 111 -825 111 B P13-32 Date & Time hour Data v Lookup & Reference ="customers/"&unit ="customers/"&unit unit&"s" =unit&"s" =unit&"s" =unit&"s" Review Summary Output Ө C V Math & Trig View More Functions customers customers P13-35 + D M08_qa_Colbert SolverTable for Mac Name Manager MacBook Pro Define Name v Use in Formula v Create from Selection E Distribution of number in system ="n (customers)" 4 Tell me =(1-$B$12) $B$12^E11 MAT Trace Precedents Trace Dependents Remove Arrows ✓ F P(n in system) 160 Show Error Watch Formulas Checking Window G H Distribution of time in queue ="t (in "&unit&"s)" 2 E Share Calculation Calculate Options + 75% Calculate -$B$12*EXP(-$B$6 (1-$B$12) H11) P(wait>t)
JA Insert Function 827 7 & Outputs 1 Renting a copier 2 3 Inputs (for slow system) 4 Unit of time S Arrival rate Service rate 20 11 Mean time per service 12 Traffic intensity 13 14 Summary measures 15 Expected number in system 16 Expected number in queue 17 Expected time in system 21 Cost analysis 22 Employee cost/hr 23 Rental cost/hour 18 Expected time in queue 19 Percentage who don't wait in queue 20 24 25 Waiting cost/hour 26 Total Cost/hour 27 28 29 30 31 32 33 34 Direct outputs from inputs Mean time between arrivals 35 36 37 38 39 40 41 AutoSum Recently Financial Logical Used 42 43 44 45 x ✓ fx A Ready P12-10-Slow A P12-10-Fast |?| AUG 16 V 2 Al 15 4 Formulas -1/85 -1/86 =85/86 Text -812/(1-812) =B12^2/(1-812) =815/B5 -B16/85 =1-B12 -822 B6 P13-32 825+823 v B Date & Time hour V Data Lookup & Reference ="customers/"&unit ="customers/"&unit unit&"s" unit&"s" V unit&"s" unit&"s" Summary Output Review el Math & Trig C V P13-35 customers customers all View More Functions V + D MacBook Pro M08_qa_Colbert SolverTable for Mac Name Manager Define Name v Use in Formula v Create from Selection E Distribution of number in system "n (customers)" 4 Tell me MAP Trace Precedents Trace Dependents FRemove Arrows ✓ =(1-$B$12) $B$12^E11 Pin in system) + W 160 Show Error Formulas Checking Window Watch G H Distribution of time in queue ="t (in "&unit&"s)" 2 + Calculation Options 77% Share -$B$12*EXP(-$B$6*(1-$B$12) H11) 08 C Calcu Calculau Plwait>t)
Transcribed Image Text:JA Insert Function 827 7 & Outputs 1 Renting a copier 2 3 Inputs (for slow system) 4 Unit of time S Arrival rate Service rate 20 11 Mean time per service 12 Traffic intensity 13 14 Summary measures 15 Expected number in system 16 Expected number in queue 17 Expected time in system 21 Cost analysis 22 Employee cost/hr 23 Rental cost/hour 18 Expected time in queue 19 Percentage who don't wait in queue 20 24 25 Waiting cost/hour 26 Total Cost/hour 27 28 29 30 31 32 33 34 Direct outputs from inputs Mean time between arrivals 35 36 37 38 39 40 41 AutoSum Recently Financial Logical Used 42 43 44 45 x ✓ fx A Ready P12-10-Slow A P12-10-Fast |?| AUG 16 V 2 Al 15 4 Formulas -1/85 -1/86 =85/86 Text -812/(1-812) =B12^2/(1-812) =815/B5 -B16/85 =1-B12 -822 B6 P13-32 825+823 v B Date & Time hour V Data Lookup & Reference ="customers/"&unit ="customers/"&unit unit&"s" unit&"s" V unit&"s" unit&"s" Summary Output Review el Math & Trig C V P13-35 customers customers all View More Functions V + D MacBook Pro M08_qa_Colbert SolverTable for Mac Name Manager Define Name v Use in Formula v Create from Selection E Distribution of number in system "n (customers)" 4 Tell me MAP Trace Precedents Trace Dependents FRemove Arrows ✓ =(1-$B$12) $B$12^E11 Pin in system) + W 160 Show Error Formulas Checking Window Watch G H Distribution of time in queue ="t (in "&unit&"s)" 2 + Calculation Options 77% Share -$B$12*EXP(-$B$6*(1-$B$12) H11) 08 C Calcu Calculau Plwait>t)
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