PA 1c. Decision VariablesabcdCalculated values0.21110.531110.09760.docx

PA 1c. Decision VariablesabcdCalculated
values0.21110.531110.09760.16019TotalObjective
Function0.860.940.930.850.90772Constraints1111110.774-
0.094-0.093-0.0850.09077>=0-0.0860.846-0.093-
0.0850.40847>=0-0.086-0.0940.837-0.0851.90E-17>=0-0.086-
0.094-0.0930.7650.04539>=00.94-2.790.22693>=00.86-1.86-
2.00E-16>=0-0.129-0.141-0.13950.72256.90E-17>=0
a.
Let the weights be a, b, c and d to midterm, final, individual
assignment and Participation respectively.
Korey would like to maximize the course grade. Therefore the
course grade (Maximization):
=0.86a + 0.94b + 0.93c + 0.85d
Restrictions to course grade working: a+b+c+d=1
The weights must be non-negative, Non negativity constraints:
a, b, c, d ≥ 0
The four components for each should determine 10% of the sum
of the grade at least.
0.86a ≥ 0.1 (0.86a + 0.94b + 0.93c + 0.85d)
0.86a ≥ 0.086a + 0.094b + 0.093c + 0.085d
0.774a – 0.094b – 0.093c -0.085d ≥ 0
0.94b ≥ 0.1 (0.86a + 0.94b + 0.93c + 0.85d)
0846b ≥ 0.086a + 0.094b + 0.093c + 0.085d
0.846b – 0.086a – 0.093c – 0.085d ≥ 0
0.93c ≥ 0.1 (0.86a + 0.94b + 0.93c + 0.85d)
0.93c ≥ 0.086a +0.094b +0.093c + 0.085d
0.837c – 0.086a – 0.094b – 0.085d ≥ 0
0.85d ≥ 0.1 (0.86a + 0.94b + 0.93c + 0.85d)
0.85d ≥ 0.086a + 0.094b + 0.093c + 0.085d
0.765d – 0.086a – 0.094b – 0.093c ≥ 0
Here it is three times the particular assignment grade.
0.94b ≥ 3(0.93c)
0.94b ≥ 2.79c
0.94b – 2.79c ≥ 0

Midterm grade must count at least twice as much as the
individual assignment score.
0.86a ≥ 2(0.93c)
0.86a ≥ 1.86c
0.86a – 1.86c ≥ 0
The presence of the grade should be less than the 15% of the
whole grade.
0.85d ≤ 0.15(0.86a + 0.94b +0.93c +0.85d)
0.85d ≤ 0.129a + 0.141b +0.1395c + 0.1275d
0.7225d – 00.129a – 0.141b – 0.1395c ≥ 0
b.
The complete optimization model is Course grade
(Maximization):
= 0.86a + 0.94b + 0.93c + 0.85d
a+b+c+d=1
0.774a – 0.094b - 0.093c – 0.085d ≥ 0
0.846b – 0.086a – 0.093c – 0.085d ≥ 0
0.837c – 0.086a – 0.094b – 0.085d ≥ 0
0.765d – 0.086a – 0.094b – 0.093c ≥ 0
0.94b – 2.79c ≥ 0
0.86a – 1.86c ≥ 0
0.7225d – 0.129a – 0.141b – 0.1395c ≥ 0
c.
Therefore midterm weights should be 21%, final weights 53%,
individual assignment 10%, Participation should be 16%.
The maximum course grade is 90%.
PA 5b.Rosenberg Land
DevelopmentDataOneTwoThreeBedroomBedroomBedroomUnit
UnitUnit1BR2BR3BRAvailableConstruction
cost$450,000$600,000$750,000$180,000,000Total

units325Profit/
unit$45,000$60,000$75,000Minimum15%25%25%ModelTotalU
nits Build4067162270Minimum406767Construction
cost$18,202,247$40,449,438$121,348,315$180,000,000Contribu
tion in
profit$1,820,225$4,044,944$12,134,831$18,000,000c.ModelTot
alUnits Build4981195325Minimum498181Construction
cost$21,937,500$48,750,000$146,250,000$216,937,500Contribu
tion in profit$2,193,750$4,875,000$14,625,000$21,693,750
a.
1BR = number of one bedroom units produced
2BR = number of two bedroom units produced
3BR = number of three bedroom units produced
Maximize Total Profit = $45,000 (1BR) + $60,000 (2BR) +
$75,000 (3BR)
(1BR) + (2BR) + (3BR) ≤ 325
$450,000 (1BR) $600,000 (2BR) + $750,000 (3BR) ≤
$180,000,000
(1BR) ≥ 15% ((1BR) + (2BR) + (3BR))
(2BR) ≥ 25% ((1BR) + (2BR) + (3BR))
(3BR) ≥ 25% ((1BR) + (2BR) + (3BR))
(1BR) ≥ 0
(2BR) ≥ 0
(3BR) ≥ 0
One crucial assumption is interpreting sensitivity analysis
information for changes in model parameters is that all other
parameters is that all other model parameters are held constant.
In this case the increase in budget also reflected in the budget
constraint. When we change the budget the constraint also
changes. This violates the assumption. The change causes the
budget constraint to become infeasible, and the solution must be
adjusted to maintain feasibility.
PA 19Children's TheaterShowRevenueCostMinimum Number of
Performances1$2,217$968322$2,330$1,568133$1,993$755234$
3,364$1,148345$2,868$1,180356$3,851$1,541167$1,836$1,359

21Children's TheaterShowMinimum Number of
Performances132213323434535616721Decision
variablesabcdefghijklmnCalculated
values00016.350000000000TotalObjective
function9681568755114811801541135996815687551148118015
41135918769.3Constraints1101101101116.34961101101101111
11116.34961111102217233019933364286838511836221723303
3642868385155000
Decision variables: Let a,b,c,d,e,f and g be the number of shows
of type show 1,2,3,4,5,6, and 7 at Kristin Marie Hall.
Let h,I,j,k,l,m and n be the number of shows of type show
1,2,3,4,5,6, and 7.
The objective of the Children’s Theater Company is minimizing
the cost.
=968a + 1568b + 755c + 1148d + 1180e + 1541f + 1359g
+968h + 1568i +755j + 1148k + 1180l + 1541m + 1359n
Hence,
a+h ≤ 32
b+I ≤ 13
c+j ≤ 23
d+k ≤ 34
e+l ≤ 35
f+m ≤ 16
g+n ≤ 21
The 60 performances are for the Marie Hall and Lauren Theater
for 150 performances.
The constraint is
a+b+c+d+e+f+g ≤ 60
h+i+k+l+m ≤ 150
2217 (a+h) + 2330 (b+i) + 1993 (c) + 3364 (d+k) + 2868 (e+l) +
3851 (f+m) + 1836 (g) ≥ 55000
Non negativity constraints
a,b,c,d,e,f,g,h,I,j,k,l,m and n ≥ 0
The schedule has been only show number 4 with 16.34 times
needs to be performed in order to minimize the cost.

The highest value of revenue is $55,000. No it is not possible to
achieve $60,000.
EXCEL ASSIGNMENT #3Fall 2016
Check Figure: NPV $7,505 of common stock
REQUIREMENTS:
· Complete Parts 1, 2 and 3 of P11-25A on page 545 - 546 (little
page numbers) of your textbook.
· There is NO What IF part to this assignment.
· REQUIRED ELEMENTS:
· Excel’s PV function must be used to calculate the present
value of the cash flows. Do not use the factor tables as is
illustrated in the text.
· A data block and cell referencing is required.
SUGGESTIONS
· Use the format illustrated under general information to
determine the NPV of each investment.
· There will be no ‘Factor’ column since excel will calculate
that for you.
· Under the ‘year(s)’ column, use ‘0’ where there would be a
‘Now’, since no time has passed from now. Be sure to input
the year(s) or period(s) in your data block so you can cell
reference them to your spreadsheet formulas.
· Under the ‘year(s)’ column, for any annuity, use the total
number of years for the annuity instead of the range. For
example: for the range ‘1-6’, you would use ‘6’ in your
spreadsheet instead (the end of the range).
· To calculate the present value, use the excel formula function
(PV) and NOT the tables in the textbook. See below for
instructions on how to use the PV function in excel.
GENERAL INFORMATION:
Data Block Page:
You must use a Data Block area, cell references and formulas.
You will cell reference the information from your data block

page to the analysis report in your excel spreadsheet.
Spreadsheet Analysis Format:
Linda Clark
Stock & Bond Investments
Net Present Value Calculation
Amount ofPresent Value
ItemYear(s)Cash Flowsof Cash Flows
Common Stock:
Purchase of the stock
Sale of the stock
Net Present Value
Preferred Stock:
Purchase of the stock
Annual cash dividend
Sale of stock
Net Present Value
Bonds:
Purchase of the bonds
Semiannual interest received
Sale of bonds
Net Present Value
Part 2: (Answer the question in your spreadsheet below your
analysis.) Use the following format:
Common StockNPV? (cell reference this from above analysis)
Preferred StockNPV? (ditto)
BondsNPV? (ditto)
Overall NPV

Did Anita earn a 20% return overall? On Which investment(s)
did she earn at least a 20% return? On which investment(s) did
she not earn at least a 20% return?
Part 3: (Extra Credit worth 5 pts)
You must use an excel formula function to calculate this
answer.
Please first do the calculation in excel, then summarize your
conclusion.
Other Information:
Please be sure what you turn in is a unique product. You may
work together, but you must each do your own spreadsheet. Do
NOT turn in duplicate spreadsheets. We will assume you
cheated and you both (or all) will get a zero for the assignment.
There is no date in your report.
Don’t forget to show dollar signs at the top if each column and
then again at each of the solutions you calculate.
Save your work frequently! Do not be the next person telling
horror stories about lost work! Back up your work on a disk.
SAVING YOUR FILE:
Save the original file according to the following name format:
Original data file: (Your Last Name, First Name Initial)
Excel#3.
For Example: SmithJExcel2.xls or SmithJExcel2.xlsx
(depending on which version of Microsoft you are using).
USING EXCEL TO CALCULATE PRESENT VALUE (PV)
LOGIC IF STATEMENT INSTRUCTIONS:
Present Value Function Instructions:
1. From the standard toolbar, select the button, ‘fx’. This
button will bring up a box called ‘Insert Function’.

2. Under function category, select “Financial”.
3. Under function name, find and select “PV”.
4. After completing step 2 & 3, select “ok” to bring up the box
for the PV function.
5. In the PV function box, enter in the relevant information
using cell references. For example, for the ‘rate’, put your
cursor in the ‘rate’ area, go to the data block, click on the ‘rate’
cell, and then click on the next area that information is needed.
Some of the areas will have no cell references if it is not
relevant to the calculation. When all relevant information is
entered, click ‘ok’. In the example below, the cell references
will be different from your cell references.
6. When placing the cell reference into the ‘Fv’ area, make sure
there is a negative (-) sign before the reference, otherwise your
output will have the wrong sign.
7. You will need to use the Pmt box when calculating the PV of
an annuity and you will use the Fv box when calculating the PV
of a single sum.
8. The Nper box is for the time period of the inflow or outflow.
SUBMISSION OF YOUR EXCEL ASSIGNMENT:
Put a footer on each page in the bottom right-hand corner which
includes your name and ZID#. Before submitting your Excel
assignment, check the Print Preview to make sure your report is
centered (horizontally) in the page and you have included the
footer. Make sure you attach the correct file before clicking the
submit button on Bb.
3
SimQuick
12-1 PA
Service rate is 180 per hour.

Service μ = 180 per hour
Arrival rate is 120 per hour
Arrival rate λ = 120 per hour
Utilization rate:
Ρ = λ/ μ
=120/180
=0.666
Average length of queue:
Lq = λ2 / μ (μ – λ)
= 1202 / 180 (180 – 120)
= 14400/ 10800
= 1.33
Average waiting time in queue:
Wq = Lq / λ
= 1.33/ 120
= 0.011 hour
= 1 Minute
Average length of queue in the system:
Ls = λ / μ – λ
=120/ 180 – 120
=2
Average waiting time in queue in the system:
Ws = 1 / μ – λ
= 1 / 180-120
= 0.0166 hour
= 1 Minute
Probability that there are no customers in the system:
Po = 1- 120/180
= 1 – 0.666
= 0.333
12-3 PA
a. Average number in the queue:
Lq = λ2 / μ (μ – λ)
= 102 / 20 (20-10)
= 0.5 customers
Average number in the system:

L = λ / μ – λ
= 10 / 20-10
= 1 customer
Average waiting time in the queue:
Wq = λ / μ (μ – λ)
= 10 / 20 (20-10)
= 0.05 hours
Average time in the system:
W = 1 / μ – λ
1/ 20-10
= 0.10 hours
Probability that the system is empty:
Po = 1- λ/ μ
= 1 – 10/20
= 0.50
b. If λ ≥ μ, that is the rate of arrivals is at least as great as
service rate, the numerical results become nonsensical. This
means that the queue will never average out but will grow
indefinitely. That is why if average arrival rate becomes equal
to average service rate, the bank manager should consider
adding a second drive through window.

b.
12-4 PA
a.
Average waiting time in the queue:
Wq = λ / μ (μ – λ)
= 2 / 3 (3-2)
=0.67 hours
b.
Average time in the system:
W = 1 / μ – λ
= 1 / 3-2
= 1 hour

c.
Average number in the queue:
Lq = λ2 / μ (μ – λ)
= 2 2 / 3 (3-2)
= 1.33 customers
d.
Probability that the system is empty:
Po = 1- λ/ μ
= 1 – 2/3
= 0.33
12-7 PA
Please see 2nd Attachment for detailed results.
Answer:
From the above output the average waiting time in line is 45.77
min while in line 2 is 15.58 min on an average, 93% of the time
the inspector 1 and 90% of time the inspector 2 are busy while
51% of time adjustment worker is busy.
Other FeaturesOther FeaturesInput Details:Output Details:5012
Resources
Discrete Distributions
Custom Schedules
Return to Control Panel
Changing Distributions
Scenarios
Buffer Tracking
Optional random seed (1 to 32,000)
Show results details (<= 200 sims.)
Hide results details
Results details
Num. times to sample inventory (10 to 200)
Yes
No
Calculate sample st. dev.

Note: The sample st. dev. can be used to construct confidence
intervals for population means and to perform hypothesis tests.
Model ViewModel View(Note: Cannot edit model
here)Simulation controls:Time units per simulation
g120Number of simulations g5Entrances:1Name gDoorTime
between arrivals gExp(2)Num. objects per arrival
g1Outputdestination(s) iDPExits:1Name gOutputTime between
departures gNor(1,.1)Num. objects per departure g1Work
Stations:1Name gTeller 1Working time gNor(2,.5)Output# of
outputResourceResourcedestination(s) iobjects iname(s) i# units
needed iSC12Name gTeller 2Working time gNor(2,.5)Output#
of outputResourceResourcedestination(s) iobjects iname(s) i#
units needed iSC1Buffers:1Name gSCCapacity
gUnlimitedInitial # objects g0OutputOutputdestination(s) igroup
size iOutput1Track details? gYesDecision Points:1Name
gDPOutputdestinations iPercents iTeller 150Teller 250
Overview
SimQuick
SimQuick is a freely-distributed Excel-based software package
for building simulation models of processes such as: waiting
lines, supply chains, manufacturing facilities, and project
scheduling. SimQuick is designed to be easy to learn and use,
with clearly-defined functionality. The package has been used
both to model real-world processes as well as in educational
settings to introduce fundamental concepts of modeling, process
simulation, and operations management.
For an example of a SimQuick model and more details on
SimQuick visit the website: SimQuick.net.
SimQuick models consist of linked combinations of five basic
elements. The element types are Entrances, Exits, Work
Stations, Buffers, and Decision Points. You have a lot of
discretion in how these elements are combined to build a model

of a process. Characteristics of the elements are entered into
SimQuick by filling in tables. Statistical distributions are a key
characteristic; they capture the uncertainty inherent in almost
all processes: arrival times of people at a service, times to
process a document or machined part, demand for a product in a
store, and so on.
SimQuick is accompanied by an inexpensive 125-page booklet
that covers the basics of process simulation and how to build
models using SimQuick. Information on the booklet and how to
order it can be found at SimQuick.net.
David Hartvigsen
Mendoza College of Business
University of Notre Dame
[email protected]
Control PanelSimQuickControl Panel© David Hartvigsen
2016Enter/Edit Model:Elements:Simulation controls:Time units
per simulation gNumber of simulations gSimulation(s) aborted
Run Simulation(s)
Clear Present Model
Entrances
Work Stations
Buffers
Decision Points
Exits
Results
Custom Schedules
Generated Schedules
Resources
Run Simulation(s)
Clear Model
Entrances
Work Stations
Buffers
Decision Points

Exits
View Results
Other Features
View Model
Discrete DistributionsDiscrete Distributions(Note: Percents
columns must sum to
100)1234567891011121314151617181920Values ¯Percents
¯Values ¯Percents ¯Values ¯Percents ¯Values ¯Percents
¯Values ¯Percents ¯
Return to Other Features
EntrancesEntrances1234567891011121314151617181920212223
24252627282930313233343536373839404142434445464748495
0Name gName gName gName gName gName gName gName
gName gName gName gName gName gName gName gName
gName gName gTime between arrivals gTime between arrivals
gTime between arrivals gTime between arrivals gTime between
arrivals gTime between arrivals gTime between arrivals gTime
between arrivals gTime between arrivals gTime between

arrivals gNum. objects per arrival gNum. objects per arrival
gNum. objects per arrival gNum. objects per arrival gNum.
objects per arrival gNum. objects per arrival gNum. objects per
arrival gNum. objects per arrival gNum. objects per arrival
arrival gNum. objects per arrival
gOutputOutputOutputOutputOutputOutputOutputOutputOutputO
utputOutputOutputOutputOutputOutputOutputOutputOutputOutp
utOutputOutputOutputOutputOutputOutputOutputOutputOutput
OutputOutputOutputOutputOutputOutputOutputOutputOutputOu
tputOutputOutputOutputOutputOutputOutputOutputOutputOutpu
tOutputOutputOutputdestination(s) idestination(s)

idestination(s) idestination(s) idestination(s) idestination(s)
idestination(s) idestination(s) idestination(s) idestination(s) i
Examples
ExitsExits12345678910111213141516171819202122232425262
72829303132333435363738394041424344454647484950Name
gName gTime between departures gTime between departures
gTime between departures gTime between departures gTime
between departures gTime between departures gTime between
departures gTime between departures gTime between departures

departures gTime between departures gNum. objects per
departure gNum. objects per departure gNum. objects per
departure gNum. objects per departure g
Examples
Work StationsWork

Stations1234567891011121314151617181920212223242526272
829303132333435363738394041424344454647484950Name
gName gWorking time gWorking time gWorking time gWorking
time gWorking time gWorking time gWorking time gWorking
time gWorking time gWorking time gOutput# of
outputResourceResourceOutput# of

outputResourceResourcedestination(s) iobjects iname(s) i# units
needed idestination(s) iobjects iname(s) i# units needed

idestination(s) iobjects iname(s) i# units needed idestination(s)
iobjects iname(s) i# units needed idestination(s) iobjects
iname(s) i# units needed idestination(s) iobjects iname(s) i#
units needed idestination(s) iobjects iname(s) i# units needed

iname(s) i# units needed i
Examples
BuffersBuffers1234567891011121314151617181920212223242
526272829303132333435363738394041424344454647484950N
ame gName gName gName gName gName gName gName
gName gName gCapacity gCapacity gCapacity gCapacity
gCapacity gCapacity gCapacity gCapacity gCapacity gCapacity
gCapacity gCapacity gCapacity gCapacity gInitial # objects
gInitial # objects gInitial # objects gInitial # objects gInitial #
objects gInitial # objects gInitial # objects gInitial # objects

tOutputOutputOutputOutputOutputOutputOutputOutputOutputO
tOutputOutputOutputOutputOutputOutputdestination(s) igroup
size idestination(s) igroup size idestination(s) igroup size
idestination(s) igroup size idestination(s) igroup size
idestination(s) igroup size iTrack details? gNoTrack details?

gNoTrack details? gNoTrack details? gNoTrack details?
gNoTrack details? gNoTrack details? gNoTrack details? gNo
Examples
Decision PointsDecision Points(Note: Percents columns must
sum to
100)1234567891011121314151617181920212223242526272829
303132333435363738394041424344454647484950Name gName
tOutputOutputOutputdestinations iPercents idestinations
iPercents idestinations iPercents idestinations iPercents
idestinations iPercents idestinations iPercents idestinations

idestinations iPercents i
Examples
ScenariosScenariosScenario
Variables123456789101Scenarios2345678910111213141516171
81920212223242526272829303132333435363738394041424344
45464748495051525354555657585960616263646566676869707
17273747576777879808182838485868788899091929394959697
9899100
Choices for Scenarios:
Nor(m,s), Exp(m), Uni(a,b), Constant, Dis(i), Cus(i), ChDist(i),
Unavailable (for Time between arr/dep at Ents and Exits, and
for Working time at WSs)
Changing DistributionsChanging DistributionsUp to 50 different
distributions can be entered in each
table.123456789101112131415161718192021222324252627282
9303132333435363738394041424344454647484950Times

¯Distributions ¯Times ¯Distributions ¯Times ¯Distributions
¯Times ¯Distributions ¯Times ¯Distributions ¯Times
¯Times ¯Distributions ¯Times ¯Distributions ¯
Choices for Changing Distributions:
Nor(m,s), Exp(m), Uni(a,b), Constant, Dis(i), Cus(i),
Unavailable (for Time between arr/dep at Ents and Exits, and
for WSs)
ResourcesResourcesName ¯Number available
¯1234567891011121314151617181920
Custom SchedulesCustom SchedulesA Custom Schedule can
have at most 1,000
arrivals/departures1234567891011121314151617181920Times
¯Quantity arriving/departing ¯Times ¯Quantity
arriving/departing ¯Times ¯Quantity arriving/departing ¯Times

arriving/departing ¯
Data Val
listsEntrances12345678910111213141516171819202122232425
26272829303132333435363738394041424344454647484950515
25354555657585960616263646566676869707172737475767778
79808182838485868788899091929394959697989910010110210
31041051061071081091101111121131141151161171181191201
21122123124125126127128129130131132133134135136137138
13914014114214314414514614714814915011234567891011121
31415161718192021222324252627282930313233343536373839
40414243444546474849502Name gName gName gName gName
gName gName gName gName gName g3Time between arrivals
gTime between arrivals gTime between arrivals gTime between

arrivals gTime between arrivals g4Num. objects per arrival
g5OutputOutputOutputOutputOutputOutputOutputOutputOutput

utOutputOutputOutput6destination(s) idestination(s)
i78910111213141516Exits1234567891011121314151617181920
21222324252627282930313233343536373839404142434445464
74849505152535455565758596061626364656667686970717273
74757677787980818283848586878889909192939495969798991
00101102103104105106107108109110111112113114115116117
11811912012112212312412512612712812913013113213313413
51361371381391401411421431441451461471481491501123456
78910111213141516171819202122232425262728293031323334
353637383940414243444546474849502Name gName gName
gName gName gName gName gName gName gName g3Time

between departures g4Num. objects per departure gNum. objects
per departure gNum. objects per departure gNum. objects per

departure
gBuffers123456789101112131415161718192021222324252627
28293031323334353637383940414243444546474849505152535
45556575859606162636465666768697071727374757677787980
81828384858687888990919293949596979899100101102103104
10510610710810911011111211311411511611711811912012112
21231241251261271281291301311321331341351361371381391
40141142143144145146147148149150112345678910111213141
51617181920212223242526272829303132333435363738394041
4243444546474849502Name gName gName gName gName
gName gName gName gName gName g3Capacity gCapacity
g4Initial # objects gInitial # objects gInitial # objects gInitial #

gInitial # objects
utOutputOutputOutputOutputOutputOutput6destination(s)
igroup size idestination(s) igroup size idestination(s) igroup
size idestination(s) igroup size idestination(s) igroup size

idestination(s) igroup size i78910111213141516Dec
Points12345678910111213141516171819202122232425262728
29303132333435363738394041424344454647484950515253545
55657585960616263646566676869707172737475767778798081
82838485868788899091929394959697989910010110210310410
51061071081091101111121131141151161171181191201211221
23124125126127128129130131132133134135136137138139140
14114214314414514614714814915011234567891011121314151
61718192021222324252627282930313233343536373839404142
43444546474849502Name gName gName gName gName gName
gName gName gName gName
utOutputOutputOutput4destinations iPercents idestinations

idestinations iPercents i567891011121314Work
Stations1234567891011121314151617181920212223242526272
82930313233343536373839404142434445464748495051525354
55565758596061626364656667686970717273747576777879808
18283848586878889909192939495969798991001011021031041
05106107108109110111112113114115116117118119120121122
12312412512612712812913013113213313413513613713813914
01411421431441451461471481491501511521531541551561571
58159160161162163164165166167168169170171172173174175
17617717817918018118218318418518618718818919019119219
31941951961971981992002012022032042052062072082092102
11212213214215216217218219220221222223224225226227228
22923023123223323423523623723823924024124224324424524
62472482492501123456789101112131415161718192021222324
25262728293031323334353637383940414243444546474849502
Name gName gName gName gName gName gName gName
gName gName g3Working time gWorking time gWorking time
gWorking time gWorking time gWorking time gWorking time

gWorking time gWorking time gWorking time g4Output# of

outputResourceResource5destination(s) iobjects iname(s) i#

iname(s) i# units needed
i6789101112131415EntrancesRowsColumnsLabelsSort of
LabelsSort correctionDistributions for Ent and Exits (Time
between)Distributions for Work StationsDistributions for Ent
and Exits (Num obj per arr/dep)Distributions for Buffer
CapacityDistributions for Initial # objs at BuffersChoices for
Buffer DetailsChoices for
WS#OutputObjsNames23Nor(m,s)Nor(m,s)Nor(m,s)ConstantNo
r(m,s)YesConstant26Exp(m)Exp(m)Exp(m)UnlimitedExp(m)No

ScenVar(i)29Uni(a,b)Uni(a,b)Uni(a,b)ScenVar(i)Uni(a,b)212Co
nstantConstantConstantConstant215Dis(i)Dis(i)Dis(i)Dis(i)218
UnavailableUnavailableCus(i)ScenVar(i)221ScenVar(i)ScenVar
(i)ScenVar(i)224ChDist(i)ChDist(i)227Cus(i)230233236239242
24524825125425726026326626927227527828128428729029329
62992102210521082111211421172120212321262129213221352
1382141214421472150Entrances72Output
destinations8292102112122132142152162758595105115125135
14515516578889810811812813814815816871181191110111111
12111311141115111611714814914101411141214131414141514
16147178179171017111712171317141715171617720820920102
01120122013201420152016207238239231023112312231323142
31523162372682692610261126122613261426152616267298299
29102911291229132914291529162973283293210321132123213
32143215321632735835935103511351235133514351535163573
88389381038113812381338143815381638741841941104111411
24113411441154116417448449441044114412441344144415441
64474784794710471147124713471447154716477508509501050
11501250135014501550165075385395310531153125313531453
15531653756856956105611561256135614561556165675985995
91059115912591359145915591659762862962106211621262136
21462156216627658659651065116512651365146515651665768
86896810681168126813681468156816687718719711071117112
71137114711571167177487497410741174127413741474157416
74777877977107711771277137714771577167778088098010801
18012801380148015801680783883983108311831283138314831
58316837868869861086118612861386148615861686789889989
10891189128913891489158916897928929921092119212921392
14921592169279589599510951195129513951495159516957988
98998109811981298139814981598169871018101910110101111
01121011310114101151011610171048104910410104111041210
41310414104151041610471078107910710107111071210713107
14107151071610771108110911010110111101211013110141101
51101611071138113911310113111131211313113141131511316
11371168116911610116111161211613116141161511616116711
98119911910119111191211913119141191511916119712281229

12210122111221212213122141221512216122712581259125101
25111251212513125141251512516125712881289128101281112
81212813128141281512816128713181319131101311113112131
13131141311513116131713481349134101341113412134131341
41341513416134713781379137101371113712137131371413715
13716137714081409140101401114012140131401414015140161
40714381439143101431114312143131431414315143161437146
81469146101461114612146131461414615146161467149814991
4910149111491214913149141491514916149Exits23Names2629
21221521822122422723023323623924224524825125425726026
32662692722752782812842872902932962992102210521082111
2114211721202123212621292132213521382141214421472150
Buffers23Names262921221521822122422723023323623924224
52482512542572602632662692722752782812842872902932962
99210221052108211121142117212021232126212921322135213
82141214421472150Buffers72Output
destinations8292102112122132142152162758595105115125135
14515516578889810811812813814815816871181191110111111
12111311141115111611714814914101411141214131414141514
16147178179171017111712171317141715171617720820920102
01120122013201420152016207238239231023112312231323142
31523162372682692610261126122613261426152616267298299
29102911291229132914291529162973283293210321132123213
32143215321632735835935103511351235133514351535163573
88389381038113812381338143815381638741841941104111411
24113411441154116417448449441044114412441344144415441
64474784794710471147124713471447154716477508509501050
11501250135014501550165075385395310531153125313531453
15531653756856956105611561256135614561556165675985995
91059115912591359145915591659762862962106211621262136
21462156216627658659651065116512651365146515651665768
86896810681168126813681468156816687718719711071117112
71137114711571167177487497410741174127413741474157416
74777877977107711771277137714771577167778088098010801
18012801380148015801680783883983108311831283138314831
58316837868869861086118612861386148615861686789889989

10891189128913891489158916897928929921092119212921392
14921592169279589599510951195129513951495159516957988
98998109811981298139814981598169871018101910110101111
01121011310114101151011610171048104910410104111041210
41310414104151041610471078107910710107111071210713107
14107151071610771108110911010110111101211013110141101
51101611071138113911310113111131211313113141131511316
11371168116911610116111161211613116141161511616116711
98119911910119111191211913119141191511916119712281229
12210122111221212213122141221512216122712581259125101
25111251212513125141251512516125712881289128101281112
81212813128141281512816128713181319131101311113112131
13131141311513116131713481349134101341113412134131341
41341513416134713781379137101371113712137131371413715
13716137714081409140101401114012140131401414015140161
40714381439143101431114312143131431414315143161437146
81469146101461114612146131461414615146161467149814991
4910149111491214913149141491514916149Decision
Points23Names2629212215218221224227230233236239242245
24825125425726026326626927227527828128428729029329629
92102210521082111211421172120212321262129213221352138
2141214421472150Decision Points52Output
destinations6272829210211212213214255657585951051151251
35145586878889810811812813814851161171181191110111111
12111311141151461471481491410141114121413141414517617
71781791710171117121713171417520620720820920102011201
22013201420523623723823923102311231223132314235266267
26826926102611261226132614265296297298299291029112912
29132914295326327328329321032113212321332143253563573
58359351035113512351335143553863873883893810381138123
81338143854164174184194110411141124113411441544644744
84494410441144124413441444547647747847947104711471247
13471447550650750850950105011501250135014505536537538
53953105311531253135314535566567568569561056115612561
35614565596597598599591059115912591359145956266276286
29621062116212621362146256566576586596510651165126513

65146556866876886896810681168126813681468571671771871
97110711171127113711471574674774874974107411741274137
41474577677777877977107711771277137714775806807808809
80108011801280138014805836837838839831083118312831383
14835866867868869861086118612861386148658968978988998
91089118912891389148959269279289299210921192129213921
49259569579589599510951195129513951495598698798898998
10981198129813981498510161017101810191011010111101121
01131011410151046104710481049104101041110412104131041
41045107610771078107910710107111071210713107141075110
61107110811091101011011110121101311014110511361137113
81139113101131111312113131131411351166116711681169116
10116111161211613116141165119611971198119911910119111
19121191311914119512261227122812291221012211122121221
31221412251256125712581259125101251112512125131251412
55128612871288128912810128111281212813128141285131613
17131813191311013111131121311313114131513461347134813
49134101341113412134131341413451376137713781379137101
37111371213713137141375140614071408140914010140111401
21401314014140514361437143814391431014311143121431314
31414351466146714681469146101461114612146131461414651
4961497149814991491014911149121491314914149Work
Stations24Names29214219224229234239244249254259264269
27427928428929429921042109211421192124212921342139214
42149215421592164216921742179218421892194219922042209
22142219222422292234223922442249Work Stations62Output
destinations7282921021121221321421526777879710711712713
71471576127128129121012111212121312141215126177178179
17101711171217131714171517622722822922102211221222132
21422152262772782792710271127122713271427152763273283
29321032113212321332143215326377378379371037113712371
33714371537642742842942104211421242134214421542647747
84794710471147124713471447154765275285295210521152125
21352145215526577578579571057115712571357145715576627
62862962106211621262136214621562667767867967106711671
26713671467156767277287297210721172127213721472157267

77778779771077117712771377147715776827828829821082118
21282138214821582687787887987108711871287138714871587
69279289299210921192129213921492159269779789799710971
19712971397149715976102710281029102101021110212102131
02141021510261077107810791071010711107121071310714107
15107611271128112911210112111121211213112141121511261
17711781179117101171111712117131171411715117612271228
12291221012211122121221312214122151226127712781279127
10127111271212713127141271512761327132813291321013211
13212132131321413215132613771378137913710137111371213
71313714137151376142714281429142101421114212142131421
41421514261477147814791471014711147121471314714147151
47615271528152915210152111521215213152141521515261577
15781579157101571115712157131571415715157616271628162
91621016211162121621316214162151626167716781679167101
67111671216713167141671516761727172817291721017211172
12172131721417215172617771778177917710177111771217713
17714177151776182718281829182101821118212182131821418
21518261877187818791871018711187121871318714187151876
19271928192919210192111921219213192141921519261977197
81979197101971119712197131971419715197620272028202920
21020211202122021320214202152026207720782079207102071
12071220713207142071520762127212821292121021211212122
12132121421215212621772178217921710217112171221713217
14217152176222722282229222102221122212222132221422215
22262277227822792271022711227122271322714227152276232
72328232923210232112321223213232142321523262377237823
79237102371123712237132371423715237624272428242924210
24211242122421324214242152426247724782479247102471124
712247132471424715247
Entrance Rules111Name ®Ent1Name ®Loading Dock 3Name
®LD2Time between arrivals ®Nor(5,2)Time between arrivals
®Exp(2)Time between arrivals ®CustomNum. objects per
arrival ®10Num. objects per arrival ®Nor(5,1)Num. objects per
arrival ®CustomOutputOutputOutputdestination(s)
¯destination(s) ¯destination(s) ¯P1DP1Buffer3P2E3

Examples:
Note: E3 will not be read because there is a blank cell above it.
Note: There must be a Custom Schedule defined with the name
LD2.
Return to Entrances
Exit Rules11Name ®Ex1Name ®Exit 5Time between departures
®Nor(10,2)Time between departures ®Exp(6)Num. objects per
departure ®25Num. objects per departure ®Nor(6,2)
Examples:
Return to Exits
Work Station Rules111Name ®WS1Name ®Lathe2Name
®BillWorking time ®Nor(5,2)Working time ®Exp(5)Working
time ®Uni(3,7)Output# of outputResourceResourceOutput# of
outputResourceResourcedestination(s) ¯objects ¯name(s) ¯#
units needed ¯destination(s) ¯objects ¯name(s) ¯# units needed
¯destination(s) ¯objects ¯name(s) ¯# units needed
¯WS21Drill21Worker11Shipping50Copier1WS35Intern2
Examples:
Note: This Work Station requires no resources.
Note: The "5" means that when this Work Station finishes a
work cycle, it sends 5 objects to WS3 (hence the number of
input objects need not equal the number of output objects).
Return to Work Stations
Buffer Rules11Name ®B1Name ®Storage Area 3Capacity
®5Capacity ®50Initial # objects ®0Initial # objects
®Nor(3,1)OutputOutputOutputOutputdestination(s) ¯group size
¯destination(s) ¯group size ¯Processor 61End Area 24Decision
Point 11Track details? gNo
Examples:
Note: Storage Area 3 sends groups (or bundles or batches) of 4
objects to End Area 2. Such a group is then considered to be a
single object.
Return to Buffers
Decision Point Rules1Name ®DPOutputdestination(s) ¯Percent
¯Buffer 110Work Station 130Exit 260

Example:
Return to Decision Points
Note: The numbers in the percent column must sum to 100.
ResultsSimulation
ResultsElementElementStatisticsScenariostypesnames1
Output TestR1Teller 2Teller 1CS3CS2CS1B3B2B1
Element Data BaseElement IndexElement NameElement
TypeTable ColumnPriorityOriginal
Index1DoorEntrance35012Teller 1Work Station45023Teller
2Work Station95034SCBuffer35045DPDecision
Point35056OutputExit3506778899101011111212131314141515
16161717181819192020212122222323242425252626272829303
13233343536373839404142434445464748495051525354555657
58596061626364656667686970717273747576777879808182838
4858687888990919293949596979899100
Resource Data BaseResource IndexName ¯Number available
¯Original Index112234567891011121314151617181920
Buffer TrackingBuffer Tracking Col. num. to graph:Col.
num.Times
The column labeled Times contains a user-designated number of
evenly-spaced times during the time span of a simulation. For
each such time, each number to the right is the overall mean
inventory level at that time for the Buffer labeling that column.
These are grouped by Scenarios, if there are any.
SimQuickSimQuick is afreely-distributedExcel-based software
package for building simulation models of processes such as:
waiting lines, supply chains, manufacturing facilities, and
project scheduling. SimQuick is designed to be easy to learn
and use,with clearly-defined functionality.The package has been
used both to model real-world processes as well as in
educational settings to introduce fundamental concepts of
modeling, process simulation, and operations management. For
an example of a SimQuick model and more details on SimQuick

visit the website: SimQuick.net.SimQuick models consist of
linked combinations of five basic elements. The element types
are Entrances, Exits, Work Stations, Buffers, and Decision
Points. You have a lot of discretion in how these elements are
combined to build a model of a process. Characteristics of the
elements are entered into SimQuick by filling in tables.
Statistical distributions are a key characteristic; they capture the
uncertainty inherent in almost all processes: arrival times of
people at a service, times to process a document or machined
part, demand for a product in a store, and so on.SimQuick is
accompanied by an inexpensive 125-page booklet that covers
the basics of process simulation and how to build models using
SimQuick. Information on the booklet and how to order it can
be found at SimQuick.net.David HartvigsenMendoza College of
BusinessUniversity of Notre [email protected]
PA 4A medical device company is allocating next year's budget
among its divisions. As a result, the R&D Division needs to
determine which research and development projects to fund.
Each project requires various software and hardware and
consulting espenses, along with internal human resources. a
budget allocation of $1,300,000 has been approved, and 35
engineers are available to work on the projects. The R&D group
has determined that at most one of the projects 1 and 2 should
be pursued, and that is project 4 is chosen, then project 2 must
also be chosen. Develop a model to select the best projects
within the budget. ProjectNPV ($)Internal EngineersAdditional
Costs
($)16000009196000268000012400000355000077000044000004
1800005350000822500067250001027500073400008130000
Solution

Let us define Xi=1 if project I allocated and 0 otherwiseOur
objective is to maximize NPV from the project. Hence our
objective function is Since the total budget is $1300000, we
have:A maximum of 35 engineers can work hence we add the
following constraint:The following are also additional
constraints:Constraint 1: At most one of the projects 1 and 2
should be pursued. Hence we haveConstraint 2: If project 4 is
chosen, then project 2 must also be
chosen.ProjectNPVEngineersCostsAllocation160000091960000
26800001240000013550000770000144000004180000153500008
22500006725000102750001734000081300000Available3513000
00Used3645000Constraint 11<=1Constraint
21<=1Model:Selected0111010TotalCosts $ - $4,00,000
$70,000 $1,80,000 $ - $2,75,000 $ - $9,25,000
Engineers01274010033NPV $ - $6,80,000 $5,50,000
$4,00,000 $ - $7,25,000 $ - $23,55,000
ConstraintsProjects 1&2Projects 2&4Constraints10The projects
chosen are therefore 2,3,4 and 6.
PA 6Soap box is a local band that plays classic and
contemporary rock. The band members charge $600 for a three
hour gig. They would like to play at least 30 gigs per year but
need to determine the best way to promote themselves. The
most they are willing to spend on promotion is $2500. the
possible promotion options are as follows: playing free gigs,
making a demo cd, hiring an agent, handing out fliers, creating

a website. Each free gig costs them about $250 for travel and
equipment but generates about 3 paying gigs. a high quality
studio demo cd should help the band book about 20 gigs, but
will cost about $1000. A demo cd made on home recording
equipment will cost only $400 but may result in only 10
bookings. A good agent will get the band about 15 gigs, but will
charge $1500. The band can create a website for $400 and
would expect to generate 6 gigs from this exposure. They also
estimate that they may book 1 gig for every 500 fliers they hand
out, which would cost $0.08 each. They do not want to play
more than 10 free gigs or send out more than 2500 fliers.
Develop and solve an optimization model to find the best
promotion strategy to maximize their revenue. Cost
$BookingsMaximumPlaying Free Gigs250310Making a Demo
CD: High Quality100020Making a Demo CD: Home
recording40010Hiring an agent150015Creating a
website4006Handing out fliers4012500Define Xi, ith option is
selected. The objective is to maximize the revenue:We should
select either a high quality CD or Home recording CD. We
define Xi=0,1 for i= 2,…,5 and X1 and X6 are integers. The
constraints are:Finally we include binary and and nonnegative
integer restrictions:Xi= binary for all i= 2,…,5Playing Free
Gigs0Making a Demo CD: High Quality0Making a Demo CD:
Home recording1Hiring an agent0Creating a website0Handing
out fliers52The band should make a home-recording CD and

should send 52 fliers to maximize revenue.
PA 9Anya is a part time MBA student who works full time and
is constantly on the run. She recognized the challenge of eating
a balanced diet and wants to minimize costs while meeting some
basic nutritional requirements. Based on some research, she
found that a very active woman should consume 2250 calories
per day. According to one author's guidelines, the following
daily nutritional requirements are recommended.
SourceRecommended intake (grams)Fatmaximum
75Carbohydratesmaximum 225Fibermaximum 30Proteinat least
168.75She chose a sample of meals that could be obtained from
the quick service restaurants around town as well as some that
could be purchased at the grocery store. FoodCost/Serving
$CaloriesFatCarbsFiber ProteinTurkey
Sandwich4.695301473428Baked potatoe
soup3.39260162316Whole grain chicken
sandwich6.3975028831044Bacon turkey
sandwich5.997702884547Southwestern refrigerated chicken
wrap3.692208291521Sesame chicken refregirated chicken
wrap3.6925010261526yoghurt0.7511021905Raisin bran with
skim milk0.4270158812Cereal bar0.43110222011 cup
brocolli0.5250.34.62.62.61 cup carrots0.5550.25133.81.31
scoop protein powder1.2912045017Anya does not want to eat
the same entrée (first six foods) more than once each day but
does not mind eating breakfast or side items (last five foods)

twice a day and protein powder based drinks up to fur times a
day for convenience. Develop an integer linear optimization
model to find the number of servings of each food choice in a
daily diet to minimize cost and meet the nutritional targets.
Define Xi number of serving per day of ith food where i= 1,
2,…,12. the objective function is to minimize the cost, that
is,The constraints are:We finally include non negativity and
integer restrictions: FoodTurkey Sandwich0Baked potatoe
soup0Whole grain chicken sandwich1Bacon turkey
sandwich1Southwestern refrigerated chicken wrap0Sesame
chicken refregirated chicken wrap0yoghurt1Raisin bran with
skim milk0Cereal bar01 cup brocolli21 cup carrots01 scoop
protein powder4Anya should take one serving whole grain
chicken sandwich, 1 serve bacon turkey sandwich, I serve
Yoghurt, 2 servings 1 cup carrot and 4 serve 1 scoop protein
powder based drinks so as to minimize costs and meet
nutritional targets.
CB_DATA_Crystal Ball DataWorkbook VariablesLast Var
Column0 Name: Value:Worksheet DataLast Data Column
Used4Sheet
RefERROR:#REF!ERROR:#REF!ERROR:#REF!ERROR:#REF!
Sheet Guid13d74b3c-49fd-4e04-b61c-c4e06823b133d62c2521-
6493-4c8f-b82b-7e25a26e977a23c4bb72-1a2b-4066-9a97-
f0ff1480e4d82510245a-8c2b-42b4-a947-683ad7c4aee0Deleted

sheet countLast row used28313131Data
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Block_7.0.0.0:1㜸〱敤㕣㕢㙣ㅣ搷㜹摥㌳㝢攱捥㤲ㄴ㘹㔱扥挸㜱㙣挶㤷㌸㌱
㔵㕡㤴慤㍡㑥愲戰扣㔸ㄷ㥢ㄲ㘹㤱㤲㘳㌸挱㙡戸㝢㐶ㅣ㙢㘷㠶㥥㤹愵㐴挷㠰㡤挴
㠹㙢戴㐹㠰摣㄰挷㑥敢ㄸ㐱㠰扣愴敤㡢㙢扢㜹㈹㄰㈰㐹攱〰㝤㐸ㅦち昴挱つ㝡㜹
㘸ㄱ〸㈸㔰昸㈱㐰晡㝤㘷㘶㜶㘷㜶戹㐳㝡㙤户㜴挱㈳敦捦㌳攷㌶攷㥣晦㝡晥晦㡣
㜳㈲㤷换晤ㅥ㠹㝦㤹ち捣摣戴扣改〷搲㥥㥣㜳ㅢつ㔹ぢ㉣搷昱㈷㘷㍣捦搸㕣戰晣
㈰㡦〶愵慡㠵㝡扦㔸昵慤㈷㘵戹扡㈱㍤ㅦ㡤㡡戹㕣戹慣㙢愸攷㈰晣㡤挶て㍡㝢つ
ㄵ〰㔶收㘶ㄷ㔷ㅦ挷愸换㠱敢挹㐳攳攷挳扥挷愶愶㈶愷㈶敦㍤㍡㜵㘴昲昰愱昱戹
㘶㈳㘸㝡昲㤸㈳㥢㠱㘷㌴づ㡤㉦㌵㔷ㅢ㔶敤㈱戹戹攲㕥㤲捥㌱戹㝡昸㥥㔵攳摥㑦
㑣摤㝢昴愸㜹晦晤㥦ㄸ挲慢㜳㘷收㘶㤷㍣㘹晡敦搱㤸㐵㑥昹摥㜹㔹戳戸㌶㈹㍤换
戹㌸㌹㌷㡢晦ㄲ昳挷搳㝤㤳换㙢㔲〶㝣戵昴愴㔳㤳扥㡥㡥㠳昶㡣敦㌷敤㜵㙥㥥㙥
ㅦ挷㔲㙢㠶ㅦㄴ敤㌹搹㘸攸㜶㍣㙡搹㕥挴摥㌵㡣捤㈱㝢㔹㍡扥ㄵ㔸ㅢ㔶戰㔹戲㔷
㌰㔰㝤搸㍥攷换戳㠶㜳㔱㥥㌱㙣㔹戴㑦㌴慤㝡㈱㑣戹晣㥤昱㄰挹㠹愹攵㑦捥昸昶
摣㥡攱愹ㄹ昹摣㤸㡣戶挷扤㕡扡敤㙤扤挷攵搴搵ㅢ㌸收ㅤ扤摢愱收扣攱戵㕡㑥昴
㙥ㄹ㉤㍥㍤㠳扢㝢户㑦散㔱扡捦挷㝢昷㔱㕢㤹㙥㉤〶㈳晡㔶㍢㡡挵攸㈵㠲〱㠲㌲
〱ㄱ愸㔷〸〶〹㠶〰㐴攱扦挰㈵挹㡥慣搲慡㠶㔶㕤搵慡㌵慤㕡搷慡㔲慢㥡㕡昵愲
㔶㕤搳慡㤶㔶㝤㕣慢㕥㐲㥢㌸㤵〷〶戴㈸晤昲扦㝦晢㤵㠷愶愶㑦晦攰昹㝦㝤攳㜳
㕦挸扦㍤戴て㡤ㅥ㡥㈶㌵敦ㄹ㤷㐱㙡㙤㉡〶㐷昰摦昶㕣〱愶㌰㡦㥡昷㤹㔳㔳昵愳
㠷㡤㝢㡣㈲㤷㤵㠱晣ㄴ愱㡣愲敤㤰昹㠸攵搴摤换ち㜷㌷捤ㅡ扥㙣㙦摣㐴㔴㌷敢㌶
㥤扡晦愱慤㉢㤷〳㈳㤰㌷㜶搶戵〷改敡戶っ戶㤲扥㝡摦捤㥤摤捥ㅢ㡤愶㥣戹㘲㠵
搵ㅦ敥愸戶㤷㍣㜷戵㜷敤㜱㑦㍥搱慡敤㥡搱っ㠴摡㠶ㅡ扢㙢㤵㘱㔵㌸慦昱戹㌵搷
㤷㡥㥡摥㠴扤㘴搵㉥㐹㙦㔹㔲㈴捡扡㕡敡戵慣㡡戸㝥㘲搱挱㐲挱慤昵㕢㤳愵收〳
㔷〲㌰戳慣㘳扥敢搲ぢ㌶㔷㡣搵㠶扣㉥搵㈴㝣㈷㉡づ愶㡡㡦扢戵愶㍦攷㍡㠱攷㌶
搲㌵㌳昵つ〳㤲愶㝥摡慤换㐲㈱愷㠴〲〴㙥㍥㉦㐴敥慥摥扣愰㄰㤱㐰㌱ㄹ昹㠶㌴

搹㑤㥥挵敡戰㡡㠶㈴㑤㙡户㙦㌳ㄸ攷慢㘴㑣〶〷㈶搶㐴晤挱㤷㝥㙣㥢㘱㕢㤸㝢㝦
ㅢ㙢摡㔸戴晡〷㌶愴ㄳ㥣㌴㥣㝡㐳㝡㤹摡㑦㜰㐶晡〸㐰昱㉡〴㐲捦摤愳慡ㄳ㔷挴
㘶昱戲㔵て搶㑡㙢搲扡戸ㄶ愰っㅡ戲㕣收搶㜶㈵晤ㅡㄴ改晢〹挶〰㉡㤵㕣改〰ㅢ
㤵㉡㐸戹㈲愵㔳〶㉦愷〴㌹晢愵㜸㜹挸㍣㙥㌵〲ㄹち攵ㄱㄳㄸ〹戵㥡㐲摦㌰㐹搴
㌳㙡愱挲㌸㘰捥㠱㑡つ换〹㌶摢㝣摢挵㈵㈱ㄱ敤挹㠲㕤㈷ぢ㈸ち搲昲㈰㠳搷㐰㌴
ㅤ搲㈰扢㜱㠲㠸挸〶ㄹ㥡ㅤ㈳愷㠹㡣敤㌳㘴〴摡㈷㠹㤰慤て昷㤶ㄱ㈴昶㙥㈲㘵愷
㥥晣戸㈷捤戶戲攵㐳㘹㜶㉤㌶㑥扦㡥攰㝡㠲ㅢ〸づ〲㠸㝦㠳㠴愳㤴㐳㍥㥤昴て攱
㔹扦㠹攰挳〰㤰㑦㍡㘵㑥㈴慡㘸㐳敤挴㡥㘴扢㘱搸挹捡㈸づ㐵ㄱ㉤攳㤶㥤㌹㙣㉢
㐴㐷㔶攷敥搰戵〵愵㘳㍦摡㥢㌶㤳换㈱㐵㘶㌴㑤慥㜵㥢愶挹㡤㘰搳㍥昵搶㉤攸慡
㡦ㄳ㝣〴愰愲摦㑡〸攵㐲㠳㜷㘷ㄶ㍤㑤捡て㠴㔹ㄴㅡ㐳㝤㉡昸㠸㤰㜹〴挸㄰㜲㕤
挷㤷㍤ㅢ㥡收攰㠴昹㠱户愱て昵收敦〸改ㅤ㝡㜳㑦敦搰㕦昴づ慤攸摢挰㕥攲㥦㝡
敡㤸㍢㔰慤㝦㤴攰㑥㠰づㅤ挳搳昷㍢昵ㄴ㈸戳搸㑥㘰㙥㍦扤㉥捡捡㕤搹㕣㤷㑡〳
つ㤹㉢㠶㜷㔱〶昰㘰㥣㥡㠷㉤散㝡㥥㙣攰㔰㕢㔷〵㍣扦㕣㥦㉥昴㡦㝢慥捤昲㍤ㅢ
搹晦㐰㈸㠶㐲㐱换攷㍡㙣攴っ㕢㌳攱㜳㑡㔰づ㜵昰㍤扤㠵㐴愲㔳㥡扣搸㉦晢㝣戹
㈷㐹晡㤰㈴ㅦ挷戶敡㜷〱㐰㑡㠸㝦攸㈹㔱づ戱搹ㅦ愸㘶㘹㡢㤵ㅥ扥㡣搳㐹㠷て戱
㑢㡥っ㠶づ摢㔹昸て晣㘱㝢搹戲㕢挲㘲搰㕥㤲㕥つ扥〵慢㈱㉢愱㕢㤶愲㘶㑦㔶㝣
㐰㘴㐵㍥摦㜵㥥捥昰慦㈹㍡改㤰ㄲ㤹摣㥥㔹㤹㜱ㄶ㙦ㄳㄵ摤㤰ㄴ㉡ㄹ慥愱㤶〴㈲
攵戱敤㥥㠸改㐳挴摣㡤㡤搳てㄳ㑣ㄱㅣ〱㈸晥ち㤲㘶愷ㅢ捦㜰搸挰〶㕤摡搵㙡慥
㑣㌴㈸ㄷ攱㥢㍤㠵搵㔱扥收て〹敥〳攸㌰㝦攸㠰捣㈰㐴㠵昲〴㈱慡㌰㠶㜹摥㤲㤷
㐹〳晢㑣〴㤶收㥡㝥攰摡㡣㉣つ㥢昳敥ㄹ㌷㤸户晣㜵㐴愲挶捣㈸昳挸㥡㜴㐰㕤ㅥ
㙣㥦㡥㌲㜷㝤㕤搶㜵㜳搹㙤㐲戴㥤㥡摦つ〷㜳㙣〷㙣㐹㜵㌶搷〴㔲㝦攷㘳っ㈱戰
搳捡摦㑡㙦散㡥扣摦㍣昴㡤戴㜷㜴挵ちㅡ㜲搰っ㤹㡥昹戲㠹㕤㐴攴愰㍥㘰慥慣㜹
㔲捥て㥢㈷㍣慢摥戰ㅣ㐹㘴挰挶㘴戰㙥㐱㕥㐴㤴㘰挹㘵っ搰㜵㠶捤ㄵ捦㜰晣㜵㠳
〱挵捤晤愹㈷ㄵㄶ㈹㥡戳㤶攳攳㌵ち㡢捣㡦㤸换㙢敥㘵㐴㙣㥢戶㜳挲㔸昷㜷〵㔶
㐸昴㘱㔲愸ㄱ㥡搰㌴㔱搶捡晤攲㠷〷昲㕣㡥扣㔷㈰㔰戸捡ㄵ改㌳捦搰摥戴敢愳ㄸ

つ敤㜴捥㘹〸搱愳㔶㘱㍥㔳ち㤳㔳昵晢搹攷㤳〰て㥥㌸㜷慡ㅤ㤹㝢㔷㌱敢㈲扤晣
ㄹ㌲㕥㤱㐵㉢㄰㐲ㅦ摤扥㤰㔴㔸㐶捡〱〷〲攳㝣敡㈴扦㡡愹摡㤰晡昶戵戳挷ㄱ㐹
ㅡ㌲ㄷ㡣㔵搹㐰㍣摡㌶㠲㝤攱〳捤㔸摢㘸昸㔱摤㥣㙢摢〶㐹㡢㘴戹㕣㌳㐸挱㌳捤
挰㍤㙤㌹扡〹愰攸㉦㉡㌲慥愰挸戸愲㡡㠶捣戳っつ慡㍣挷㜲㉦ㅡ㥥ㄵ慣搹㔶慤捣
〷㠶敦㜶〵㑤㠲挹㈹㜹攳ㄴ换㡣昱づ㙢晥ㅣ㑣㌶㝦ㄲ攸㥥㠴ㅣ攵搶ㄱ晤愰㕣㑤㤴
昰㑦昴改㔸㠲㠰㔱㥥㔲晤搳ㄸ慤愸㙥㐷㐰攴愸㜴㌵扥㠳㜱昵㘹㤴㠴㐲㠸㔸捦㈰ㄱ
㜸〵ㄳ㐲㥥㉥敥㤲㜹捥戱〲㘰㡦ㄸ㍢㙥〵昳㍥㔰づ㠰慣㍡摥摥愸戰㥡攸㌴搱搲ち
户㜴㔷愵搴挴捤摤昵㐹扤㜱晢ㄶ搵愱㐶㐹㈸㤲敤ㅡ㈹捤戲挵ㅣ㜷㤳慡ㄱ㑡㜱挷摡
㐶㘴戹㑤摢晢㑥㈹昲㉥ㄴ㤳愲㤹㥣晥ㄹ㐵㈸〸昴㐶㍡㡡㍥晢㙣昲㐸㐴㙣㘸〳㔴愸
愷挲戲攱㈸㈴㜸ち搷㑥敡戲ㄲ㍤㠱扦昷㐵搹挵㘶㤰慡㌱慥㡣㐵㌵㌳㡤挶愲〳㉢愱
㘶㜸昵㕤挲搲㔸㕢愸㘱ㄴ㜷昶慢晤挳敤㑤㌰㘲挴㠶っ㡢㘴昸㠱挱㠶㘰慥㐴㐴㤵搶
搹㌰户扡㔵㕣收搳㘹㘹㌸ち〳换㐱㝤㕥㙥㈸㌳慣㙤挹㡦愹づ慤搳愲㤲愳扡㌹戳敡
㐳愵〷㤴攳㔱㑥㌱戸㙥㥥愵㕢ち㤷ㄸ㈰㜶愳摣㔲㉤㐰㘸户㌵〰㑦〶扢〷㍢搸㤱㌰
㜴㐲敢㡣ㄲ戴㤴㐱戸改㐵㤰㜷晡挴㈸〴愹愹搲㙦愷挵昷㕥㘰晡昱㜴㉥捥㐴㑣挴㜰
㔷㠶昵〰攴㈶㈳㤳攴愲戱㌸㘰ㅥ㑡㌶㈵戴㠶攲㌲㥡ㄸ挳㌴昹扣〰户㜸ㄸ换ㅡ㈱摢
㌴㜰捦㉤戰愰㑤ㅢ㥢晢捣㔳㑥慤搱慣㑢愵㡡㘳㔹慤㌴昲慥挰㤷扡〲ㄸ㜲㔳挶扥㐴
㥢㜲ち㐷㈹㉥㤹㐸敡摦敥搶愷搱㕤〹㌹㡣ㄱ慡㍥〶㈰㌳摣㜲㉡㈰搶㜵㑦㠱昶攱晥
昶〵〶㜵㜹づ㈲慤慢㠸戲㙣〱昷昱㕡㔱㘴挵㙤㠹㘶ぢ敥㠲㑢㥢㍤㔱㜴搲ち㡢㜶〵
㡥戰捥㔰攰㤵㑡㌰㐶晡攴づづ㤲扢ㅡ㐵㜷慦㍥慤ㅥ㜳㔷㠱ち㠵〱挱ㄸ㉦㑦㐱㌹散
㉡ㄸ㠹〶户搶戶扡〵愳扦戴扣昵ㄹ〰挱㌰㌰つ㕡戴っつ㥣㌹攴户㌷㜰㙥㐱慢㡣〸
㘹㌲㤸捡ㄸ攵ㄸㅣ昶㐰ㅡ戸㠹〷改ㄵㄷ㑡㈸㌸愰㉥㠶挵㜷ㄳ㈷㙣ㅣ㠱㕣敦扡㡥挲
㈵㈳挰昵ㄷ攷㘰㐷昱㑣扤㑥㜳ㄷ晥戹㕤㠱㔵㕣摤〸捤搱〳ㅤ㤷戲搴㥡㘸摦摤搶㔱
ㄱ㕤ㄶ㍣㌲㍦㜹搲〸㙡㙢换挱㘶㜸㜱慢㕦㤲㈸晥ㄴ晥㠸㉤摦㑥㥢戹攰昰㈲敡〶昷
扥㜲挹㜱㉦㍢㙡㕥㐵㥦户晥㐰㈱戸㐲㌹挰㐹㔶㜲扦挷㍦㤵戴㕣昱㙦㌰攲㑥愶捤〱
摡づㄲ㡥愳㔲㈸つ挶㤱捦愰ㄳ搸敥慤㕢〳愴㤳〳ㅤ㜴愲〴挱ㅥ愱㌸ㄷ摦㌳㐲ㄱ㙦

〰慤㈴㤶昰㐸㡥㍤晦ㄱ㔸㕦扣㡥ㄲ㈲ㅣ捦㤱ㄸ㈹㝥〴戹っ搴㈹㐱ㅥ㕤昱攰㠵㤰晦
㍦㔸㡡戹㜹㑢㜶晡㕦㘰㘶昱㕡㈷㡡㙥㈶㡡晥扡ぢ㐵㠲搷㐰ㄴ晦㍥㠸㑣㥣㡡っ捦扥
愳㐰㌸搷戴㜷〰㝤摦㉦晣晥ㅦㅥ㐰ㄷ㈲攲㔰㌶ㅡ㐲㙤㜷攰戹㘵㈲攴扢㑣〴〶敦㤵
㠹㜰ㅡㄹ挱㈸㝥㘸㈲㐴㍥㤰㐵ㄴ㙣㙦㈲㌰戶㤷㘱〸㈶㐲慤〹户〶㑦㘰搷搹昴㡦㥤
挴挵㕢改㈳㥥て愵攵捦挱㈳㜵㝤㜷昱㤲攱ㄹ昶㐱㔵㝥挲㤳㔰㘶摥ち㙥㜲慢㉥散㜱
攳㤶㌵慡搳ㄶ扥㡡搸换扥攷㑦搹搹晤㜵㘰㉡㑣愱晢㕥㤴㐵改㕤㜸㑡〴捦つ戹㉦ㅣ
昸挹㠹㝦㝥昲搹㘹摥㔶㡢㘸戵㜸ㄷ昲晤㠴散㘹㑦㈰愸㥢戸㈸㜲㉤㍦捣㌹㡤㑦㤴慣
昵㠶㥣㌵㍣㘵〵昹扡ㅤ㘷㐳挲㑢㄰㘶㐸㝣扢挱挴挴扤㠷搰挴㥣散㜰㜷慡て㥢㤴㡢
㜰㌲㌱㜱攵搳㡢挳㠶愲愷㈲敢搳摡㉣晥㈵㔴搱㍢㥣㐸摡㑡攴愹㤳㐹㠸扦攸搴㜵㐷
愹敢挲㠳っ挳晥戱㤴㐲晣㠱ㄴ㤲㍣挸昰㐲㠰㤲㔲㘷㤱㈹摥つ㤰ㄱ㔹敢っ昱搲ㅦ戰
㈷〴㘴敢搲㕦㥦ㅦ戱㘰ㄷ㠱挵搸ㄷ摦敦㠹㤶戶㘸慣㥡ㄸ慡㔵㌶捤㌲㌲敡昰挲㠲愹
戸㌴㘵改ㅣ㐱改㡥摤㔱㝣挹戰ㅤ〶摥㐲挶㉥摡昴戵㔵散〷㥣㈶㙥㝥㐰捦㤴㤴挲㜰
昶戳ㄸ〷㔲ㄵ愳ぢ㥢㔶挲㈲挲㤱㌰摢敡㌴ㄸ㔵㐱㘷㌹〷㜱㉡㐵昰㡦㕦ち戱㝥愲㍤
昴戵㥤㌵搴㜱捥〰ㄶ挸ㅦ散慦㥢㌳ㄸㅢ㙦㈵挷㐰挲敥愸㔵㌹扣ㅥ㝥づ㕤戸攸㥣搰
摢㔹昵㉣㡥攲㑦捣㔹㜹慤㑢晦㌳㝡慤㌸敢㍣㝢㌳㡣㥤搲晦㥦㐵挱戶晡㕦㌰昶愶㄰
昹㘸㤴攱㐳㤱昱㤳㙤㐳㌶摣ㄱ㜸戶ㄱ扣㔱〷㘳㕤㘵ㄹ昲づ㜳换昸㜸㌵慣㔶ㄲㅣ㝥
慦㐲攷搵㠸㔶㕦摡戶㠳㍤〵㈰㘳㐳挵ㅦ㐱〴昵散㥦㤶㕢昱改戶昴ㄸ㍡ㅥ㌸㙤搵㍣
搷㜷捤㘰㝣ㄹ㐱摦㜱㝥㝢㘶挲收㤹ㄱ㍦散ㄴ㙡户㘱㈷㠶㍥㡦㍥㘷ㄶ㈱戰捦挸攰扤
㡡㐵㌲戲戰戳㐸〶扦㐳ㅡ㑤㠴㤷愸ㅤ晣㙢捣㠷㥢㐶〳㥦慥㉥挲搷ㄹ戰㘸㔷㈸扢搰
攳摣㜹㐳㠳㕢㠷㍢㕡て挱ㅦ㈴ㅢ㤳〸㡥愹㈵㍣昶㜹敥㙢攷ㅥ愴摢㐶㙢昳搹戲㍦㥦
㕢愵昸ち㜰扡戳户愴㐹㠶敦攴ㄷ挹ㄵ扤㑡㠸㑢晢搳昸扢㜳〷㉤㐷ㅢ〳㥤㐷ㅦ㜴搳
ㄱ㌶搱㠰晢㙣〷搱敦ぢ攸㉡㘶〸昰搳㡤㈸挳〷㐱㉦ㅦ㔹㔱晣ㄹ㤶㐵〶㐰㍥㔷慡〱
昴愶敡㤷戶愲敡搱㔸㈰ぢ㥥㌱㐸㡥ㄵ昱㈲ㅡ㜲扢挲㘵㠳㈵戸㙣愱捥ㄲ挸敢㜱て攴
㜳㠲㘷〹㌵㤱敦愲㐳㙢㈲ㄶ㑡㝢㑦攴㍢㕢㑤㐴搰ち㔰ぢ㑤㡥㍦ㅡ㙢ㄱ扤㠱㙡摤㈶
㜰〸㕣㠰ㄱ㡡㐵捡㥡㔲ㄸ㕡㜸㥤㤸㐱晡晢攸敦㕢搳扦㝡㤳改㍦愷㠵ㄲ㠴愸㑡㑦㥥

㠲㔰㑤晥敢挹挹㝢㈸敤㍤昹慦㙥㌵昹㔱捡㐸捥㐴て〰㠶昳愲㡡㍦㙡㌱㑤㘴戸㡦晣
㠹ぢ〴昸愵㘶㌱㙡愰㐴昵扤㡣っ晡㜲挳㔵慢㉢挸挴㝤㡢㕣㝦挶挷㍤捡㍥攲㐵㐸晡
㜲㑡愱㌳戶ㄴ㙡挵戲ㅤ㜹㘱㜷㠵㙣挰㤲昸戵㙣㑦㤱㕥敡㌳挲㉦㥥㡢ㄱ㜳昲㘴晣攵
㤴ㄶ挵㥣㐰ㄸ愱㐵㑡晡攱㐶㡡慦挴㡤晦敡搵戶换ㄴㄵ㐸愰㥥戰㌱改㑣㌵晥㜲摣昸
〸扥捡㔲㙤㜲扣㐱挰昴㔶摣㤸昴愸ㅡ㍦ㅢ㌷晥㡦㈳〷㕢㡤㘳㍡っ㐷㉥㤲㐸㌲㙣㕤
㘵晤㈷扥搰ㅥ㐱昳愲㐹晤㌹㘸㠶挵㤴㥣㉡㜴摣㔰ㅡ㜴〸㤷㐱㍣㝣㈳扤㠰扢㑤戸〲
〲㈱ㅢ晥慦ㄲ㑥攱捥搳扣ㄱㄸ昸〴㝡〳挱㘶㑦㔷㑦散㕣㌲ㄷ㍤ㄴっ㤸愷㝣㥣愹敡
扢㡡㐴㘰づㄴ挲晤摤挶㈹㥦㘱㍡戶昷㈳づ㤲㘹扣㐳搲㥦昲㔰㠱㤵㠲昸㘲㡣搹摣㌳
㙤㥡搱㥦〶㜲㈰ㅤ〱㤹搱㥦〱っ〳㌱扣慤㥣ㅢ㈵晦㉢收晥㈲㉢扥㐴昰㉣㐰㐵㤰搹
㐹〷愵㉦〳㡣挴晦愳㡡昱つ攵㉦搱挴㤳昱换㤲㘴愴㍦挷づ㝦っ㤰㠷晢㔶㐴㐴㔸搱
㥦㐷㐹昲愵ㄴㅣ敡愵㝦挲㡡㍦㈵昸㉡㐰愵挸挹敥㜸搷戸愶㍥㌵搷搷搰㔵㍣㐳㠰㥦
晥昵㈸挳㠷㈲昷攱㔳扤㙤㘵ㅥ㠵攳て晢ㄱ敡㑣㝤挱晦〰扥挸摦攴愲昳昸ㅦ㤲ㄴ㤵
㘱㕦搰㍥搹摦㔸㘴〲摡攴敡户㡥捤㝥ㄷ攳㜰㕤敤〸ち㐷愴㔲㈹㙢㈵㐱㝣㜳挱挲挵
ㅢ昸㤶㘳慡㐲〸搲㠰慡㜰愲㡡㘹ㄴ攸摦㘴㔳攲㤸㜸搲扦挵㈷愲㔶㙤攲户愳っㅦ〴
昱慡扡㍦ㅥ㜵㡦㕦㐸㕣慢ち慢攳㠵挴扦慡㔸㑢扥昰〵づ愶㤰㠵㑣㕡㉢ㄱ㘹㡡㠶㕥
㐴㘶㌸㍦挲戹㍤㠲㥦㜶㐵搴㉥搴㉦㕣㜸㝢愴㌰㝥㘳攱戳㝦㌴昴挲㕢㝦昷㥢㙦晣晡
㜳挷晥晤㜷㉦扤昴敢㝦昹挶㥢扦晢改敡戱㥦扦昲捡捦ㅥ晣昳㌷㝦戳摦㝣㔹㝢昵敤
㠵㤷㥦㥡扡昴搴ㄳ收戹扢㑥㍣昵攸攳て㑦㉤㕤㌳㤱捦てっ摣㌹昶㡢ㅢ㍥㌶晡捣ㄳ
慦㠹扦晤挷敢ㅤ愱㤶㡢ㄷ愴愷挱㘵慢㘹㝣ㅦㄹ㑣㠳㌳㝥㕦愷挱攵慡㡤㕡㡤㌶㙡ㄶ
〵㘵昸㌴㌸〱㔵㘱愴㉢〶晦〷㕥散戴〹㜸〱敤㕢㙢㙣ㅣ搷㜵摥扢扢㌳摣扢㝣慤ㅥ
㝥㍢㌶㘵㑢戵㘳ち㉣㈹㠹㤱㔵㥢㤵挸愵㐴㌳愱㈴㥡愴ㅦ㘹㙢慣㠷扢㜷挴戵㜶㜷攸
㤹㔹㡡㜴㥣摡㜹搴㙤㤱戶㘹ㅤ户㡤ㄳ愵㜶㡣愰㜱㕡ㄴ㙥晣㈳㜰搳愲㡤㠱戴㌵〲改
㑦㘱戸㡦㕦㠶㔳愰㐵攲㍡㔲㠲愰㐶攱㕡晤扥㍢㌳摣㈷㈹㠹㔶㔰晥挸㐸㝢收扥攷摥
㜳敦㍤攷㍢攷㕥挶㐴㉣ㄶ扢㠰㠷㙦㍥㐹〶㙥㥣㕤昱㝣㔵ㅥ挸㍡愵㤲捡晢㐵愷攲つ
㡣扡慥戵㌲㔵昴晣〴ち㤸戹㈲昲㍤㈳攷ㄵㅦ㔳愹摣㤲㜲㍤ㄴ㌲㘲戱㔴㑡挶㤱捦㌲

晣㘵愲㠸㘴㑣㈶㐹㔰㉡搶㘵㠲捣㘵挷㡥捦㍦㠲昶㘷㝤挷㔵扢晢敥て㕡ㄹㄹㅡㅡㄸ
ㅡ搸㌷㍣戴㘷㘰㜰㜷㕦戶㕡昲慢慥ㅡ愹愸慡敦㕡愵摤㝤搳搵昹㔲㌱晦㌱戵㌲攷㥣
㔴㤵ㄱ㌵㍦戸㜷摥摡㜷攷搰扥攱㘱晢挰㠱㍢扢㍡搰昲戱散搸戴慢㙣敦㑡戵㤹㘲㥢
挷戳㘳〳挷㤴㝦愵摡㤴㘸ㄳ㑤㡥㍢㘵慢㔸戹㐲㡤ㅡ攴昲昰戸捡ㄷ㌹ㅤ㑡戹挵捡㠹
〱㜴扢㠱搱㠸敤ㅦㄸ昵扣㙡㜹㤱㌳㥢㔵愵搲㡣戲㌹㐴㔹ㅥ昷晣㘹换㉤㝢㕤㘵昲㑦
戹慡㤲㔷㕥㑦昹昰㜲㕥㤵挲㠲㕥慡㝣扦攵ㅥ戳捡㉡挹㐰㙦㌹㤸挳挹㠲慡昸㐵㝦愵
扢㝣㥦愷㘶慣捡〹挵㈲㐶㜹愲㕡㉣㠸㘴ㄲ晦㘳㠹摢摡昵㑣㑦ㄴ晡㔳捥㉥㔸慥慦㘳
㥣挲愱㜶㘵敢㤶㡢ㅥ㐵㐳扦戸愴晡㥡㙡㜱捥㘶㡢攵㡦㈹户愲㑡晣〸㠷搹摦㔴㐸㌳
㈸㤸㠷㔵㑥㐵挳攱㉣㠹捥㜰㍢㜰㉣晣㡡㤹〶ㄹ㤸㜳㡢ㄸ㘶戵㘴戹扢㡦ㄶ㉢㈳㐳晢
昶てづ敥㥥㉡㥥㔴愵愲昲晣㤱愱攱㐱挴㡦㕡换〸敤ㅤㅣ㤴㥤愸㈳扢㔸扢ㅢ愴攷昸
愲㜲㉤ㅦ昳搳㤷㜵㍣㕦昶㌰户ㄷ㐴㈴捦㘱㌷搶㝦㤱ㄵ攳㌹㉢㥥㥢㡦攷昲昱㕣㈱㥥
㔳昱㥣ㅤ捦㥤㠸攷ㄶ攲戹㘲㍣昷㐸㍣㜷ㄲ㘵愲㈷搵搱ㄱて㥦㥥扥扢㥦㝡攱捣㡦㈷
㥥㝥㙣晣挳慦㡣扣昱㥡挱つ戸户摤昰㥢㌹㝢〴㍢㌲㙦㜹㝥㌸改㥣㤱㉢扢㈶㉥扥㈴
㡥戸昹㥦晤㤲挰㐷慥挸㤲㤰㕢挰㈱戹ㄵ挴摣㐶㌲敤㍡㜶搱㤷摢㤹㝡ㄵ㠸㄰㍦挰戴
㜲㙡愷晦敥挲攷挶㍥昱愱愳㕦㝥㉤昷搷攷㈷㕥㝥㕤㔰ㅥ㜲摦㥡搷㠰散㙡㕡㔵㝢敢
㤷搴摥㝤㝡㍤敤ㅢ㤴搷愲愸扣㡥㤵慥〷戹晡㔸戵㍣慦摣㍥挷敥慢㔶㡡扥搷㠷㝤敢
慢㠲扣㠱愵㙥〴ㄱ攲晢攱搷㝦㜲挷改㘷晥扥㜴昵攴㌳㍦㝤攷散㡢搷扥戴慢敢㈶㘴
摦ㅢ慥敦㜱搷㍡㠵ㄵ㔹ㄳ㐶㤰挰晣㜷㜱㈹っ㈱㙣て摢晢敤愱愱挲昰愰戵搷㌲戸㘸
㉦㜵扢㘷㔰戶换㝥愰㔸㈹㌸愷昴晥扦㜱捣昲㔴㙤敥晢挳扣㌱愷㕡㈹㜸㌷戴捦㥣昵
㉤㕦㕤摦㥣㔷㙢愴愵摡㉣愴愳昲昴昷㙥㙡慥㜶扦㔵慡慡搱攵㘲㤰晤愱愶㙣挸㐶㘷
㝥敤摣㈳慥㝡㜴㌵户愵㐷愳㔰愷㑢扡敤㤶㔱〶㔹㐱扦晡戲ぢ㡥愷㉡扡㝢晤攵改㘲
晥愴㜲㘷ㄵ㤵戱㉡攸愱㕥挵慣㔰㐰昷ㅦ慦㘰愰㄰戹㠵㕢敡㔳敤挳换扥慡ㄴ㔴〱晤
㠵戴昱㔷收慣昹㤲扡扡愱㐸昰㑤㘴㕣搷㤰㝣挴挹㔷扤慣㔳昱㕤愷搴㤸㌳㕡㔸戲愰
ㄴち㐷㥤㠲㠲㑣㑦昲㠹㠹㔸㈲㈱㐴散㡥㜶㤲㠵敤㝡〳㝡㈲敡愶㤸〲攵摡挶㘵㌷㌰
㠳搱㘱ㄴ㈵挵㌵ㄹ摦㜹㤱挶㜴扢㙣收挳㙢ㄷ慣ㅢㄳ㤱ぢ㑢摦扥㜶㘹摤挷搵㤹晢搹

ㄶ㡥挷户㠵愳㍦扣㠴捤㝡㡦㔵㈹㤴㤴扢㉥敥ㄲ散㤱扣ㄹ挴㜸ㄳ扢㜹㑤敥㔱挶㡢㘵
戱㘲㥣㉡ㄶ晣〵㜳㐱ㄵ㑦㉣昸㐸〳㌶㑢愵挸摡㤶㐷敥㐰㤲扣㠵攴㔶㤰㜴㍡㘶敥㘴
㈱㌳㉤㜷〵㜱㠳㡡敢昲㔵㌲搱㥦搴㄰〰㜸捤㌳捡搰㉡㕥㈲搱㙥㤴昷㔸摥㠲捦攵戹
㙥㈶㤵慦晣〵㤲摢㐰っ㉡捤㡢㙡㝣㉡搵㈴㠱㑤㜷㜹㕣搹ㄶ攰愴摥摤挲㌲捡〱㐲ㄹ
㔷㕥㕥ㄲ捡㑣㘲慦㉣㥢〸㘱昳㜷㤵戹晡搵戲㍦㙥昹㔶㐷ㄹ愰〸戳㈴㔱愸㕦搷ち㐲
慣搹慤搳愲摡改㌰㠶ㄶ㌲㍡㔸搷㑡愷㑥〸㕡挲挶挱㝥㠹㈵㐲扡晥㈰搰㜷敡㈸戳㜹
愱㌷㠲ㅢ㘰慥挲㠴慡捣慤㉣㉡㡦挵㔳收扡慣㙣摥㕥㙣散㜸㝥晥㍥扦㔸昲〶搰搳〹
搷愹㉥㕥搱㜶搰㈷㜹㍢㐸昴ㄸ晦㡣㔵㝣改㘳愲㕤搲戱挴戹挹攵戰㤴ㄱ㘳㡡㈴㤸㤲
㕣慤㘸散〲㕥晡㤱扢昱㑡慦㤷㘷㜰㔹㕣づ㄰搴㔶㑢ㄹㅣ㥡㜳㤵㠶戶㈹ㅤ〱户扢换
て㌸敥挹㜹挷㌹挹昵搴愳㘳摥㠲㔲㍥攱㘲㘷〸㡦㌵っㄶ㈲㤱㘸㐰㜶㜵戸㤲㐰搳ㅣ
〴改ㅥ㉤㤵晡愲ㄶ㍤㜳〸㐹〹〰㔷㜳て〲摢愷㔵挵捡捤㠰㔴㜲㐷昷㡦敥ㄹ㔸㉥㜹
换攲㉣㐶㑥㘴戱㘳搷敥㌷扥㔰昸晣搴㉢晤扦扥敢㠵捡ㅦ㍦㈶捥㠴ㄹ㉤㌰㤰㘰㘵ㅤ
敤摣㠰扣〸㘱ㅡ戴㜳㤷㝤愴㔸昲㤵慢〵㜰慦㡤㔷㘰㙥攸㜸㌷㤵㡥㙢攵〳㈰扦摤捥
㐲敦挰扥昱㔷㙡㥡戸㐵敦〵㙡攱攷摡㝤搳㘹㜷慤摢ㅢ㌴晣㍡摡ㄳ㡢愶㐹扦慦㕦戸
㙥ㄱ㔱戱戵摤㡢㝡㐹つ愰攵挶㐵挶昲捤㠲㐳ㅢ㜱慢攵敢ㄷ㈱㑢て慥慤昵戹搸㕢ㄷ
㈹㉢慤愹㘱㝦㡥㑦摡昹㠵〲㝣㌲っ挶挹㡦㤰散㈷戹㤳攴〰㠸昸〷〸㈳攲㤶晦㝡て
搲ち〹摦〵㌸昸扥ㄶ攱㜷戱捣摤㈴㈳㈰㐰ㅦ㕡㥥〳㝣ㅣ㐴搴㍣〴搲ㅢ㤹愳㝤挱ㄲ
㑢挷〴㑤㉤㠲ㄲ㌹㑡㌲挶㔸ㄶ攴搸㍤慡〴慣㝢愵㍣㍦〶愵摦晡摡ㄹ敢㠷㝤戹扡㍣
扢㔲挹㉦戸㑥〵ㅥ㌱㠲㠶搱㍣㕣㈷㥥戰捣昲㤴㤳慤晡㘶昹㥥㈲㕥㕤攵ㄹ戵愸㉣㍦
ぢ㕢〶㠸㘴ち㈶戶挶ㅢ㤳㠵攵晦㑦㍣ㄲ㈳㘸㠴㤹㔸㠳㈴愲㜹昷〶挸㈰㘴敦挰戸〳
㌷㥣搲㍥㐱戲摤㌴㠱㉤㌷㈱攰㠸挹㜱昴敥戹昳㝦㜶搷慥慦扣㜴㈱㝣㍦㠱㔵愸ㅦ㐹
㔳扤ㄵ㍣㑣㈰㌵扤㕥㥥愰㐵㑦〰㈱愹戰捤㈹㤰〴㤶㠱愴㡡ㄶ㉦愳改戶摡昸㥢㘱㐶
㡢〳㠰挶扣昶づ㑤戳晥㑢㈸挶㝤㠲㜰攳㈳㘷㄰㤷戳㈴㜳㈰㜵晢攴晥㈰㉡攸㄰搰㝢
攲〱ㄶ㝡㄰㐴搰〵愰㝤㑢ㅦ㐷㈰㝡挴㥦愲㝤愲㉦扤晤攸㐱㘸㘵挲㐳㐸㑤换㜵昲〴
ㅤぢ慢㑣㤰挴㈹〱〳㑥愳攱戶っ昸㜲㤸搱散㠳㌰㘸搳㕣㠶敤愸㜹㘵摦㕦㔴愷〸㜶

㝢㙣㌸ㅣ戳㔵捦㜷㌴㌲敦戶挷㥤㘳㡥㍦㕥昴ㄶ㑢搶捡㌶㍢っ㍣戰愰㉡戰㥢㕤㤸捦
㑤㘹捥攲㈲㕣㈵昶慣㔳㜵昳㙡㜲㝣㌳搸搵㘰〷愶㑥㥢搴㜱㠱㘷㘳愶㈲戶戳挰㉡挱
ㄳ㌳㜶愰挱㘶挴㕦愷㌱㙢攰㉣㠳㠲扤㌵㡥捥ㄵ晤㤲敡戴㜵扥づ愷㙣㜰ㄱ捥㠸㐲㠷
㍤户〰㈴㍣摥㙤㑦戸挵㐲愹㔸㔱㥣っ〰㍥㝡㜱愷搴〹㌸ㅥ愶ㅤ慦㐸て㜳户㍤攷㕡
ㄵ㙦㤱㌶㔴㝥㘵㙢㐳㑣ぢ㍦挳ㅥ㉢㔶㍣㝣㐶捦㈲挳扤昶散㠲㜳ち挷て搵㜲㘵挲㕡
昴㌶挵慣㜰户〴㡦㥥ㅡㄱㄷ昱戸㐸挵㔳ㅢ㥤ㅦ搳㐶㙢搷搴ㅣ㝥㝤㔸慢扥㕢㥣慦㤲
㘹晡㐳ㄴ㈸㐹ㄲ㍤㡦㌱㠳㈶晡㍡挰㠷昰㈷㜴〹搱摤挱晥㌶㌸㙤摢㕡摥慢攷㍡㠴㍣
昲〴敢㉣㠰㝣㜴攲扥挹㥡㈳昰〳ㅤ挹ㄸ㜴㉡㌴慢㤳收搵户敡㜷愱㙣敤〹㤶ㄱ搳戸
慡戰㍢戱ㅡㄸ㙢㕥㥡㘹㕢㤷攱㉡敤愹〵㡦挰㜴敦戲愷慣㜹㔵〲㜰㈸㕢㝥㑦㄰㈱〸
㉣㕢㈵㉦捣换㍡攵戲挵㘵挷㈵㍢㥢户㑡㉡㘵㡦㔶㝤〷摥㝣㘹㠳攸戵ㄹ㈶㔹换㐸戲
㤶㜵㔲㤷㍤㐳㑦愴づ戳㉤攷㠴攵ㄶ晤㠵㜲㌱㥦㘲㠴摥挲㑤戱㕥㈱㐳戴㕡〷㐳昹㐴
昲愴ㄹ捥〴㡡ㅤ搳㍤〰㜰㐵搶㜱晡戱慡攳挲挴㍦戱㐱㐷ㄵ愴㡦㔶㉡昲ㄱ戴㘶搰ㄱ
㐴㜱愴㥦㜳搱㘱攳戹㈷㤰愲〵㤴愰㥦㠹搹㤲㈷ㄹっ昰㤷愴慢㘷㕤㉦〶搷㙣㝡捡戱
ち㐷㘰㜲㍡㙥㐷㜸㠴㤸挲搴㔲摣戸ㄹ晡㤵戲㜰㔵挲〵扡㔴㉣㈸㌷挵㠴㔹㐰戴㈴㍤
㔲㘶㌰㠷攴㑤捣㌰㍡㔳敤扥㌵ㄹ戵戵㌳戴搶敢て㐵㈷㕢摡㝦晢摥㍢〹㕢㌱慣〴愸
㉣㤱㤴㐱挴㙤㈰ㅣ㑦㔳〱㙥㜴改㠰ㄸ昴㡤㌴捦㑤愳㡢〷㡥㈰扡〹㤲晡昰㡤捥愷ㄴ
ㅣ㌵摡㙢㘵攸㠱㜴搶㜹㥢捣挰搱㤴㡡㑥昴捣㔹慣㜲㔵㐸〷㌲㤶〰㤵搳ㄱ㡦㈷㌱搵
㘶戳㉦愰攵戳㘸慣㍣慢戴ㅢ㑡搰昵㘲㉥㠲㕣捤捤㠲昶㜳㑤㘷㔹㍢㤱〷㔵扦㡡㘰搲
㘹改㈲㈹㤶ㄶ扢㐱㈳ㅥ昰っ㉤㥤搶㐲挷㐳㔰搲㐵㘹搰㝡㔸㐷㔲〰㘴搵搹㤸挴㌵愶
㝤ㅦ㑦㍣㍡昵挶㍤㔲昴搱㥤㉥ㅢ〴㐱㙤っ㕥慦㌷㜷㕤愵晥㔵攰㜰㜳㙢㔶〳㤲戸愹
㌵扦ㅥ㕡散㙣㤳ㅤ㠰㡥㍡慣㜱戱㐲ㅡ㝣戴改攳㘶㐲㈳㈲㌰づ㐲㐰㈲㜶慤㙤㑡搷昱
㥤昳晡〱戰㡢㔹㐵晤攴ㅥ㥣愰挶攴ㄲ㠲㄰〷挴㌲昲ㄴ㠲挴㌳㌴㌰搷㕦㈷㜵敥〵攲
挵㌴㌱㑤㤰搶ㅤ晡慦㈶㉢ㅥ㈴㐲㍡㡣㐱摥昷㠴挱攳㔵扦㈱挷㕡摥ㄶ收挰㌵㜷扣〲
㉤㥤户摣挲㈶ㄱ昱ㄸ㕢㠰㐶戴戴摥㈰㔲㐴㈳㝣敡〴㌳戰晦㌲㔲挸㙢摡昱㤷攳㥤愱
㑤搰㑤㜶慦㍡㙤㔲㡣ㅤ㔵㔶㐵捦挲慣㕦ㄸ㔷㑢ㅡ戶㑦㉢㘰㙥㕣ㅢ㈸愹㙤扡挲㙡㔴

PA 1c. Decision VariablesabcdCalculated values0.21110.531110.09760.docx

PA 1c. Decision VariablesabcdCalculated values0.21110.531110.09760.docx

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