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
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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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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