01a decision making
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Decision MakingDecision Making
Supplement ASupplement A
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Break-Even AnalysisBreak-Even Analysis
Break-even analysis is used to compareprocesses by finding the volume at which two
different processes have equal total costs.Break-even point is the volume at which
total revenues equal total costs.
Variable costs (c) are costs that varydirectly with the volume of output.
Fixed costs (F) are those costs that remainconstant with changes in output level.
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Q is the volume of customers or units,c is the unit variable cost, Fis fixedcosts andp is the revenue per unit
cQis the total variable cost.
Total cost =F+ cQ
Total revenue =pQ
Break-even is wherepQ= F+ cQ
(Total revenue = Total cost)
Break-Even AnalysisBreak-Even Analysis
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Break-Even Analysis cantell you
If a forecast sales volume is sufficientto break even (no profit or no loss)
How low variable cost per unit must beto break even given current prices andsales forecast.
How low the fixed cost need to be tobreak even.
How price levels affect the break-even
volume.
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Hospital ExampleHospital ExampleExample A.1Example A.1
A hospital is considering a new procedure to be offeredat $200 per patient. The fixed cost per year would be
$100,000, with total variable costs of $100 per patient.
Q = F / (p - c)Q = F / (p - c) = 100,000 / (200-100)= 100,000 / (200-100) = 1,000 patients= 1,000 patients
What is the break-even quantity for this service?
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400 400
300 300
200 200
100 100
0 0
Patients (Patients (QQ))
D
ollars
(in
thou
sands)
D
ollars
(in
thousands)
|| || || ||
500500 10001000 15001500 20002000
Quantity Total Annual Total Annual(patients) Cost ($) Revenue ($)
(Q) (100,000 + 100Q) (200Q)0 100,000 0
2000 300,000 400,000
Hospital ExampleHospital ExampleExample A.1Example A.1continuedcontinued
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Quantity Total Annual Total Annual(patients) Cost ($) Revenue ($)
(Q) (100,000 + 100Q) (200Q)
0 100,000 02000 300,000 400,000
400 400
300 300
200 200
100 100
0 0
Patients (Patients (QQ))
D
ollars
(in
thou
sands)
D
ollars
(in
thousands)
|| || || ||
500500 10001000 15001500 20002000
(2000, 400)(2000, 400)
Total annual revenuesTotal annual revenues
Quantity Total Annual Total Annual(patients) Cost ($) Revenue ($)
(Q) (100,000 + 100Q) (200Q)
0 100,000 02000 300,000 400,000
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Total annual costsTotal annual costs
Patients (Patients (QQ))
D
ollars
(in
thou
sands)
D
ollars
(in
thousands)
400 400
300 300
200 200
100 100
0 0
|| || || ||
500500 10001000 15001500 20002000
Fixed costsFixed costs
(2000, 400)(2000, 400)
(2000, 300)(2000, 300)
Quantity Total Annual Total Annual(patients) Cost ($) Revenue ($)
(Q) (100,000 + 100Q) (200Q)
0 100,000 02000 300,000 400,000
Total annual revenuesTotal annual revenues
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Total annual revenuesTotal annual revenues
Total annual costsTotal annual costs
Patients (Patients (QQ))
D
ollars
(in
thousands)
D
ollars(in
thou
sands)
400 400
300 300
200 200
100 100
0 0
|| || || ||
500500 10001000 15001500 20002000
Fixed costsFixed costs
Break-even quantityBreak-even quantity
(2000, 400)(2000, 400)
(2000, 300(2000, 300))
ProfitsProfits
LossLoss
Quantity Total Annual Total Annual(patients) Cost ($) Revenue ($)
(Q) (100,000 + 100Q) (200Q)
0 100,000 02000 300,000 400,000
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Total annual revenuesTotal annual revenues
Total annual costsTotal annual costs
Patients (Patients (QQ))
D
ollars
(in
thousands)
D
ollars(in
thou
sands)
400 400
300 300
200 200
100 100
0 0
|| || || ||
500500 10001000 15001500 20002000
Fixed costsFixed costs
ProfitsProfits
LossLoss
Sensitivity AnalysisSensitivity AnalysisExample A.2Example A.2
Forecast = 1,500Forecast = 1,500
pQ (F+ cQ)
200(1500) [100,000 + 100(1500)]
$50,000
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Two Processes andTwo Processes andMake-or-Buy DecisionsMake-or-Buy Decisions
Breakeven analysis can be used to choosebetween two processes or between aninternal process and buying those services or
materials.
The solution finds the point at which the totalcosts of each of the two alternatives are
equal.The forecast volume is then applied to see
which alternative has the lowest cost for thatvolume.
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Breakeven forBreakeven for
Two ProcessesTwo ProcessesExample A.3Example A.3
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Q =Fm Fb
cb cm
Q =12,000 2,400
2.0 1.5
Breakeven forBreakeven for
Two ProcessesTwo ProcessesExample A.3Example A.3
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Q=Fm Fb
cb cm
Q= 19,200 saladsBreakeven forBreakeven for
Two ProcessesTwo ProcessesExample A.3Example A.3
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Preference MatrixPreference Matrix
A Preference Matrix is a table that allows you to ratean alternative according to several performance criteria.
The criteria can be scored on any scale as long as thesame scale is applied to all the alternatives beingcompared.
Each score is weighted according to its perceivedimportance, with the total weights typically equaling 100.
The total score is the sum of the weighted scores(weight score) for all the criteria. The manager cancompare the scores for alternatives against one another
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PerformancePerformance WeightWeight ScoreScore Weighted ScoreWeighted Score
CriterionCriterion ((AA)) ((BB)) ((AA xx BB))Market potentialMarket potential
Unit profit marginUnit profit margin
Operations compatibilityOperations compatibility
Competitive advantageCompetitive advantage
Investment requirementInvestment requirementProject riskProject risk
Threshold scoreThreshold score = 800= 800
Preference MatrixPreference MatrixExample A.4Example A.4
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PerformancePerformance WeightWeight ScoreScore Weighted ScoreWeighted Score
CriterionCriterion ((AA)) ((BB)) ((AA xx BB))
Market potentialMarket potential 3030
Unit profit marginUnit profit margin 2020
Operations compatibilityOperations compatibility 2020
Competitive advantageCompetitive advantage 1515
Investment requirementInvestment requirement 1010Project riskProject risk 55
Threshold scoreThreshold score = 800= 800
Preference MatrixPreference MatrixExample A.4Example A.4continuedcontinued
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PerformancePerformance WeightWeight ScoreScore Weighted ScoreWeighted Score
CriterionCriterion ((AA)) ((BB)) ((AA xx BB))
Market potentialMarket potential 3030 88
Unit profit marginUnit profit margin 2020 1010
Operations compatibilityOperations compatibility 2020 66
Competitive advantageCompetitive advantage 1515 1010
Investment requirementInvestment requirement 1010 22Project riskProject risk 55 44
Threshold scoreThreshold score = 800= 800
Preference MatrixPreference MatrixExample A.4Example A.4continuedcontinued
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PerformancePerformance WeightWeight ScoreScore Weighted ScoreWeighted Score
CriterionCriterion ((AA)) ((BB)) ((AA xx BB))
Market potentialMarket potential 3030 88 240240
Unit profit marginUnit profit margin 2020 1010 200200
Operations compatibilityOperations compatibility 2020 66 120120
Competitive advantageCompetitive advantage 1515 1010 150150
Investment requirementInvestment requirement 1010 22 2020Project riskProject risk 55 44 2020
Threshold scoreThreshold score = 800= 800
Preference MatrixPreference MatrixExample A.4Example A.4continuedcontinued
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PerformancePerformance WeightWeight ScoreScore Weighted ScoreWeighted Score
CriterionCriterion ((AA)) ((BB)) ((AA xx BB))Market potentialMarket potential 3030 88 240240
Unit profit marginUnit profit margin 2020 1010 200200
Operations compatibilityOperations compatibility 2020 66 120120
Competitive advantageCompetitive advantage 1515 1010 150150
Investment requirementInvestment requirement 1010 22 2020Project riskProject risk 55 44 2020
Weighted score =Weighted score = 750750
Threshold scoreThreshold score = 800= 800
Preference MatrixPreference MatrixExample A.4Example A.4continuedcontinued
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PerformancePerformance WeightWeight ScoreScore Weighted ScoreWeighted Score
CriterionCriterion ((AA)) ((BB)) ((AA xx BB))
Market potentialMarket potential 3030 88 240240
Unit profit marginUnit profit margin 2020 1010 200200
Operations compatibilityOperations compatibility 2020 66 120120
Competitive advantageCompetitive advantage 1515 1010 150150
Investment requirementInvestment requirement 1010 22 2020Project riskProject risk 55 44 2020
Weighted score =Weighted score = 750750
Threshold scoreThreshold score = 800= 800
Preference MatrixPreference MatrixExample A.4Example A.4continuedcontinued
Score does not meet theScore does not meet the
threshold and is rejected.threshold and is rejected.
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Decision Theory
Decision theory is a general approach to decisionmaking when the outcomes associated with alternativesare often in doubt.
A manager makes choices using the following process:
1. List the feasible alternatives2. List the chance events (states of nature).3. Calculate thepayofffor each alternative
in each event.4. Estimate theprobabilityof each event.
(The total probabilities must add up to 1.)
5. Select the decision rule to evaluate thealternatives.
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Decision Rules
Decision Making Under Uncertainty is when you areunable to estimate the probabilities of events. Maximin: The best of the worst. A pessimistic approach.
Maximax: The best of the best. An optimistic approach.
MinimaxRegret: Minimizing your regret (also pessimistic)
Laplace: The alternative with the best weighted payoffusing assumed probabilities.
Decision Making Under Riskis when one is able toestimate the probabilities of the events. ExpectedValue: The alternative with the highest weighted
payoff using predicted probabilities.
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Clemens Model of Decision Analysis[adapted from Fig. 1.1]
Identify the decisionsituation &understand
objectives Identify alternatives
Decompose &
model the problemproblem structureuncertainty
preferences
Choose the bestalternative
Sensitivity analysis
Iterate or continuethe analysis?
Implement chosen
alternative
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OConnors Model
ID theDecision;
Set
boundariesfor analysis
IDAlternatives
DevelopObjectiveFunction
DevelopInfluenceDiagram
ConductSensitivityAnalysis
RefineInfluenceDiagram
Structure &ComputeDecision
Tree or RunM.C.
Simulation
Model DMsUtility
ComputeEVPI
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AlternativesAlternatives LowLow HighHigh
Small facilitySmall facility 200200 270270Large facilityLarge facility 160160 800800
Do nothingDo nothing 00 00
EventsEvents(Uncertain Demand)(Uncertain Demand)
MaxiMin DecisionExample A.6a.
1.1. Look at the payoffs for each alternative and identify theLook at the payoffs for each alternative and identify thelowest payoff for each.lowest payoff for each.
2.2. Choose the alternative that has the highest of these.Choose the alternative that has the highest of these.
(the maximum of the minimums)(the maximum of the minimums)
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AlternativesAlternatives LowLow HighHigh
Small facilitySmall facility 200200 270270Large facilityLarge facility 160160 800800
Do nothingDo nothing 00 00
EventsEvents(Uncertain Demand)(Uncertain Demand)
MaxiMaxDecisionExample A.6b.
1.1. Look at the payoffs for each alternative and identify theLook at the payoffs for each alternative and identify thehighesthighest payoff for each. payoff for each.
2.2. Choose the alternative that has the highest of these.Choose the alternative that has the highest of these.
(the maximum of the maximums)(the maximum of the maximums)
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Laplace(Assumed equal probabilities)
Example A.6c.
AlternativesAlternatives LowLow HighHigh
(0.5)(0.5) (0.5)(0.5)
Small facilitySmall facility 200200 270270
Large facilityLarge facility 160160 800800
Do nothingDo nothing 00 00
EventsEvents
200*0.5 + 270*0.5 = 235200*0.5 + 270*0.5 = 235
160*0.5 + 800*0.5 = 480160*0.5 + 800*0.5 = 480
Multiply each payoff by the probability ofMultiply each payoff by the probability ofoccurrence of its associated event.occurrence of its associated event.
Select the alternative with the highest weighted payoff.Select the alternative with the highest weighted payoff.
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MiniMax Regret
Example A.6d.
AlternativesAlternatives LowLow HighHigh
Small facilitySmall facility 200200 270270Large facilityLarge facility 160160 800800
Do nothingDo nothing 00 00
EventsEvents(Uncertain Demand)(Uncertain Demand)
Look atLook at
eacheach
payoff and ask yourself,payoff and ask yourself,
If I end up here, doIf I end up here, do
I have any regrets?I have any regrets?
Your regret, if any, is the difference between that payoffYour regret, if any, is the difference between that payoffand what you could have had by choosing a differentand what you could have had by choosing a different
alternative, given the same state of nature (event).alternative, given the same state of nature (event).
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MiniMax RegretExample A.6d. continued
AlternativesAlternatives LowLow HighHigh
Small facilitySmall facility 200200 270270Large facilityLarge facility 160160 800800
Do nothingDo nothing 00 00
EventsEvents(Uncertain Demand)(Uncertain Demand)
If you chose a smallIf you chose a smallfacility and demand isfacility and demand islow, you have zerolow, you have zeroregret.regret.
If you chose a large facility andIf you chose a large facility and
demand is low, you have a regret ofdemand is low, you have a regret of40. (The difference between the40. (The difference between the
160 you got and the 200 you could160 you got and the 200 you couldhave had.)have had.)
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MiniMax Regret
Example A.6d. continued
AlternativesAlternatives LowLow HighHigh
Small facilitySmall facility 200200 270270Large facilityLarge facility 160160 800800
Do nothingDo nothing 00 00
EventsEvents(Uncertain Demand)(Uncertain Demand)
Alternatives LowAlternatives Low HighHigh
Small facility 0Small facility 0 530530
Large facility 40Large facility 40 00
Do nothing 200Do nothing 200 800800
EventsEvents
MaxRegretMaxRegret
530530
4040
800800
Regret MatrixRegret MatrixBuilding a largeBuilding a large
facility offers thefacility offers the
least regret.least regret.
E pected Val e
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Expected ValueDecision Making under Risk
Example A.7
AlternativesAlternatives LowLow HighHigh
((0.40.4)) ((0.60.6))
Small facilitySmall facility 200200 270270
Large facilityLarge facility 160160 800800
Do nothingDo nothing 00 00
EventsEvents
200*0.4 + 270*0.6 = 242200*0.4 + 270*0.6 = 242
160*0.4 + 800*0.6 = 544160*0.4 + 800*0.6 = 544
Multiply each payoff by the probability ofMultiply each payoff by the probability ofoccurrence of its associated event.occurrence of its associated event.
Select the alternative with the highest weighted payoff.Select the alternative with the highest weighted payoff.
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Decision TreesDecision Treesare schematic modelsare schematic modelsof alternatives available along withof alternatives available along with
their possible consequences.their possible consequences.They are used in sequential decisionThey are used in sequential decision
situations.situations.Decision points are represented byDecision points are represented by
squares.squares.Event points are represented byEvent points are represented by
circles.circles.
Decision TreesDecision Trees
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= Event node= Event node
= Decision node= Decision node
1st1st
decisiondecisionPossiblePossible
2nd decision2nd decision
Payoff 1Payoff 1
Payoff 2Payoff 2
Payoff 3Payoff 3
Alternative 3Alternative 3
Alternative 4Alternative 4
Alternative 5Alternative 5
Payoff 1Payoff 1
Payoff 2Payoff 2
Payoff 3Payoff 3
EE11 & Probability& Probability
EE22& Probability& Probability
EE33& Probability& Probability
EE22& Probability& Probability
EE33& Probability& Probability
EE11&
Prob
ability
&Pr
obab
ility
Altern
ativ
e1
Alter
nativ
e1
Alterna
tive2
Alternat
ive2
Payoff 1Payoff 1
Payoff 2Payoff 2
1 2
Decision TreesDecision Trees
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Smallf
acili
ty
Sm
allf
acili
ty
Largefacility
Largefa
cility
1
Drawing the TreeDrawing the TreeExample A.8Example A.8
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Small
facilit
y
Small
facilit
y
Larg
efacility
Larg
efacility
Low demand [0.4]Low demand [0.4]
Dont expandDont expand
ExpandExpand
$200$200
$223$223
$270$270
Highdemand
Highdemand
[0.6]
[0.6]
1
2
Drawing the TreeDrawing the TreeExample A.8Example A.8continuedcontinued
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Small
facilit
y
Small
facilit
y
Largefacility
Largefacility
1
Lowde
mand
Lowde
mand
[0.4]
[0.4]
Low demand [0.4]Low demand [0.4]
Dont expandDont expand
ExpandExpand
Do nothingDo nothing
AdvertiseAdvertise
$200$200
$223$223
$270$270
$40$40
$800$800
Modest response [0.3]Modest response [0.3]
Sizable response [0.7]Sizable response [0.7]
$20$20
$220$220
Highdeman
d
Highdeman
d
[0.6]
[0.6
]
High demand [0.6]High demand [0.6]
2
3
Completed DrawingCompleted DrawingExample A.8Example A.8
S #S l i D i i #3
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Solving Decision #3Solving Decision #3
Example A.8Example A.8
Lowde
man
d
Lowde
mand
[0.4]
[0.4]
Small
facilit
y
Small
facilit
y
Larg
efacility
Largefacility
Low demand [0.4]Low demand [0.4]
Dont expandDont expand
ExpandExpand
Do nothingDo nothing
AdvertiseAdvertise
$200$200
$223$223
$270$270
$40$40
$800$800
Modest response [0.3]Modest response [0.3]
Sizable response [0.7]Sizable response [0.7]
$20$20
$220$220
Highdema
nd
Highdeman
d
[0.6]
[0.6]
High demand [0.6]High demand [0.6]
1
2
3
0.3 x $20 = $60.3 x $20 = $6
0.7 x $220 = $1540.7 x $220 = $154
$6 + $154 = $160$6 + $154 = $160
S #
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Dont expandDont expand
ExpandExpand
Do nothingDo nothing
AdvertiseAdvertise
$200$200
$223$223
$270$270
$40$40
$800$800
$160$160Lo
wde
man
d
Lowde
mand
[0.4]
[0.4]
Small
facilit
y
Small
facilit
y
Larg
efacility
Largefacility
Low demand [0.4]Low demand [0.4]
Modest response [0.3]Modest response [0.3]
Sizable response [0.7]Sizable response [0.7]
$20$20
$220$220
Highdema
nd
Highdeman
d
[0.6]
[0.6]
High demand [0.6]High demand [0.6]
1
2
3
Solving Decision #3Solving Decision #3
Example A.8Example A.8
$160$160
S l i D i i #2S l i D i i #2
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$160$160
Modest response [0.3]Modest response [0.3]
Sizable response [0.7]Sizable response [0.7]
$20$20
$220$220
Solving Decision #2Solving Decision #2
Example A.8Example A.8
Expanding has aExpanding has a
higher value.higher value.
Lowde
man
d
Lowde
mand
[0.4]
[0.4]
$160$160
Small
facilit
y
Small
facilit
y
Largefacility
Largefacility
Low demand [0.4]Low demand [0.4]
Dont expandDont expand
ExpandExpand
Do nothingDo nothing
AdvertiseAdvertise
$200$200
$223$223
$270$270
$40$40
$800$800
Highdema
nd
Highdeman
d
[0.6]
[0.6]
High demand [0.6]High demand [0.6]
1
2
3
$270$270
S l i D i i #1
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$470$470
x 0.4 = $80x 0.4 = $80
x 0.6 = $162x 0.6 = $162
$242$242
$160$160Lo
wde
mand
Lowdema
nd
[0.4]
[0.4]
$270$270
$160$160
Small
facilit
y
Smallf
acili
ty
Largefacility
Largefacility
Low demand [0.4]Low demand [0.4]
Dont expandDont expand
ExpandExpand
Do nothingDo nothing
AdvertiseAdvertise
$200$200
$223$223
$270$270
$40$40
$800$800
Modest response [0.3]Modest response [0.3]
Sizable response [0.7]Sizable response [0.7]
$20$20
$220$220
Highdeman
d
Highdeman
d
[0.6][0.6]
High demand [0.6]High demand [0.6]
1
2
3
Solving Decision #1Solving Decision #1
Example A.8Example A.8
S l i D i i #1S l i D i i #1
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Solving Decision #1Solving Decision #1
Example A.8Example A.8
$242$242
$160$160Lo
wdema
nd
Lowdema
nd
[0.4]
[0.4]
$270$270
$160$160
Small
facilit
y
Smallf
acili
ty
Largefacility
Largefacility
Low demand [0.4]Low demand [0.4]
Dont expandDont expand
ExpandExpand
Do nothingDo nothing
AdvertiseAdvertise
$200$200
$223$223
$270$270
$40$40
$800$800
Modest response [0.3]Modest response [0.3]
Sizable response [0.7]Sizable response [0.7]
$20$20
$220$220
Highdeman
d
Highdeman
d
[0.6][0.6]
High demand [0.6]High demand [0.6]
1
2
3
x 0.6 = $480x 0.6 = $480
0.4 x $160 = $640.4 x $160 = $64
$544$544
S l i D i i #1S l i D i i #1
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$160$160Lo
wdem
and
Lowdem
and
[0.4]
[0.4]
$270$270
$160$160
Small
facilit
y
Small
facilit
y
Largefacility
Largefacility
$242$242
$544$544
Low demand [0.4]Low demand [0.4]
Dont expandDont expand
ExpandExpand
Do nothingDo nothing
AdvertiseAdvertise
$200$200
$223$223
$270$270
$40$40
$800$800
Modest response [0.3]Modest response [0.3]
Sizable response [0.7]Sizable response [0.7]
$20$20
$220$220
Highdemand
Highdemand
[0.6][0.6]
High demand [0.6]High demand [0.6]
1
2
3
Solving Decision #1Solving Decision #1
Example A.8Example A.8
$544$544
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