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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 compare processes 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 vary directly with the volume of output.
Fixed costs (F) are those costs that remain constant with changes in output level.
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“Q” is the volume of customers or units, “c” is the unit variable cost, F is fixed costs and p is the revenue per unit
cQ is the total variable cost.Total cost = F + cQTotal revenue = pQBreak-even is where pQ = F + cQ
(Total revenue = Total cost)
Break-Even AnalysisBreak-Even Analysis
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Break-Even Analysis can tell you…
If a forecast sales volume is sufficient to break even (no profit or no loss)
How low variable cost per unit must be to break even given current prices and sales forecast.
How low the fixed cost need to be to break 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 offered at $200 per patient. The fixed cost per year would be$100,000, with total variable costs of $100 per patient.
Q = F / (p - c) Q = F / (p - c) = 100,000 / (200-100) = 100,000 / (200-100) = 1,000 patients= 1,000 patients
What is the break-even quantity for this service?
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400 –400 –
300 –300 –
200 –200 –
100 –100 –
0 –0 –
Patients (Patients (QQ))
Do
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(in
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Do
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(in
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|| || || ||
500500 10001000 15001500 20002000
Quantity Total Annual Total Annual(patients) Cost ($) Revenue ($)
(Q) (100,000 + 100Q) (200Q)
0 100,000 02000 300,000 400,000
Hospital ExampleHospital ExampleExample A.1Example A.1 continuedcontinued
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Quantity Total Annual Total Annual(patients) Cost ($) Revenue ($)
(Q) (100,000 + 100Q) (200Q)
0 100,000 02000 300,000 400,000
400 –400 –
300 –300 –
200 –200 –
100 –100 –
0 –0 –
Patients (Patients (QQ))
Do
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(in
th
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Do
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(in
th
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|| || || ||
500500 10001000 15001500 20002000
(2000, 400)(2000, 400)
Total annual revenuesTotal annual revenues
Quantity Total Annual Total Annual(patients) Cost ($) Revenue ($)
(Q) (100,000 + 100Q) (200Q)
0 100,000 02000 300,000 400,000
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Total annual costsTotal annual costs
Patients (Patients (QQ))
Do
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(in
th
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Do
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(in
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400 –400 –
300 –300 –
200 –200 –
100 –100 –
0 –0 –|| || || ||
500500 10001000 15001500 20002000
Fixed costsFixed costs
(2000, 400)(2000, 400)
(2000, 300)(2000, 300)
Quantity Total Annual Total Annual(patients) Cost ($) Revenue ($)
(Q) (100,000 + 100Q) (200Q)
0 100,000 02000 300,000 400,000
Total annual revenuesTotal annual revenues
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Total annual revenuesTotal annual revenues
Total annual costsTotal annual costs
Patients (Patients (QQ))
Do
llars
(in
th
ou
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ds)
Do
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(in
th
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400 –400 –
300 –300 –
200 –200 –
100 –100 –
0 –0 –|| || || ||
500500 10001000 15001500 20002000
Fixed costsFixed costs
Break-even quantityBreak-even quantity
(2000, 400)(2000, 400)
(2000, 300(2000, 300))
ProfitsProfits
LossLoss
Quantity Total Annual Total Annual(patients) Cost ($) Revenue ($)
(Q) (100,000 + 100Q) (200Q)
0 100,000 02000 300,000 400,000
© 2007 Pearson Education
Total annual revenuesTotal annual revenues
Total annual costsTotal annual costs
Patients (Patients (QQ))
Do
llars
(in
th
ou
san
ds)
Do
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(in
th
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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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Application A.1
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Application A.1Solution
TR = pQTR = pQ TC = F + cQTC = F + cQQQ
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Application A.1Solution
TC = F + cQTC = F + cQTR = pQTR = pQQQ
© 2007 Pearson Education
Application A.1Solution
TR = pQTR = pQQQ TC = F + pQTC = F + pQ
pQ = F + cQpQ = F + cQ
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Two Processes and Two Processes and Make-or-Buy Decisions Make-or-Buy Decisions
Breakeven analysis can be used to choose
between two processes or between an internal process and buying those services or materials.
The solution finds the point at which the total costs of each of the two alternatives are equal.
The forecast volume is then applied to see which alternative has the lowest cost for that volume.
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Breakeven for Breakeven for Two ProcessesTwo Processes
Example A.3Example A.3
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Q =Fm – Fb
cb – cm
Q =12,000 – 2,400
2.0 – 1.5Breakeven forBreakeven for
Two ProcessesTwo ProcessesExample A.3Example A.3
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Q =Fm – Fb
cb – cm
Q = 19,200 saladsBreakeven for Breakeven for Two ProcessesTwo Processes
Example A.3Example A.3
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Application A.2
FFmm – F – Fbb
c cbb – –
ccm m
==Q =Q = $300,000 – $0$300,000 – $0 $9 – $7$9 – $7
= = $150,000$150,000
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Preference MatrixPreference Matrix
A Preference Matrix is a table that allows you to rate an alternative according to several performance criteria.
The criteria can be scored on any scale as long as the same scale is applied to all the alternatives being compared.
Each score is weighted according to its perceived importance, 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 can compare the scores for alternatives against one another or against a predetermined threshold.
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PerformancePerformance WeightWeight ScoreScore Weighted ScoreWeighted ScoreCriterionCriterion ((AA)) ((BB)) ((AA x x BB))
Market potentialMarket potentialUnit profit marginUnit profit marginOperations compatibilityOperations compatibilityCompetitive advantageCompetitive advantageInvestment requirementInvestment requirementProject riskProject risk
Threshold score Threshold score = 800= 800
Preference MatrixPreference MatrixExample A.4Example A.4
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PerformancePerformance WeightWeight ScoreScore Weighted ScoreWeighted ScoreCriterionCriterion ((AA)) ((BB)) ((AA x x BB))
Market potentialMarket potential 3030Unit profit marginUnit profit margin 2020Operations compatibilityOperations compatibility 2020Competitive advantageCompetitive advantage 1515Investment requirementInvestment requirement 1010Project riskProject risk 55
Threshold score Threshold score = 800= 800
Preference MatrixPreference MatrixExample A.4Example A.4 continuedcontinued
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PerformancePerformance WeightWeight ScoreScore Weighted ScoreWeighted ScoreCriterionCriterion ((AA)) ((BB)) ((AA x x BB))
Market potentialMarket potential 3030 88Unit profit marginUnit profit margin 2020 1010Operations compatibilityOperations compatibility 2020 66Competitive advantageCompetitive advantage 1515 1010Investment requirementInvestment requirement 1010 22Project riskProject risk 55 44
Threshold score Threshold score = 800= 800
Preference MatrixPreference MatrixExample A.4Example A.4 continuedcontinued
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PerformancePerformance WeightWeight ScoreScore Weighted ScoreWeighted ScoreCriterionCriterion ((AA)) ((BB)) ((AA x x BB))
Market potentialMarket potential 3030 88 240240Unit profit marginUnit profit margin 2020 1010 200200Operations compatibilityOperations compatibility 2020 66 120120Competitive advantageCompetitive advantage 1515 1010 150150Investment requirementInvestment requirement 1010 22 2020Project riskProject risk 55 44 2020
Threshold score Threshold score = 800= 800
Preference MatrixPreference MatrixExample A.4Example A.4 continuedcontinued
© 2007 Pearson Education
PerformancePerformance WeightWeight ScoreScore Weighted ScoreWeighted ScoreCriterionCriterion ((AA)) ((BB)) ((AA x x BB))
Market potentialMarket potential 3030 88 240240Unit profit marginUnit profit margin 2020 1010 200200Operations compatibilityOperations compatibility 2020 66 120120Competitive advantageCompetitive advantage 1515 1010 150150Investment requirementInvestment requirement 1010 22 2020Project riskProject risk 55 44 2020
Weighted score =Weighted score = 750750
Threshold score Threshold score = 800= 800
Preference MatrixPreference MatrixExample A.4Example A.4 continuedcontinued
© 2007 Pearson Education
PerformancePerformance WeightWeight ScoreScore Weighted ScoreWeighted ScoreCriterionCriterion ((AA)) ((BB)) ((AA x x BB))
Market potentialMarket potential 3030 88 240240Unit profit marginUnit profit margin 2020 1010 200200Operations compatibilityOperations compatibility 2020 66 120120Competitive advantageCompetitive advantage 1515 1010 150150Investment requirementInvestment requirement 1010 22 2020Project riskProject risk 55 44 2020
Weighted score =Weighted score = 750750
Threshold score Threshold score = 800= 800
Preference MatrixPreference MatrixExample A.4Example A.4 continuedcontinued
Score does not meet the Score does not meet the threshold and is rejected.threshold and is rejected.
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Application A.3
Repeat this process for each alternative — pick the one with the largest weighted scoreRepeat this process for each alternative — pick the one with the largest weighted score
The concept of a weighted scoreThe concept of a weighted score
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Decision Theory
Decision theory is a general approach to decision making when the outcomes associated with alternatives are 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 the payoff for each alternative
in each event.4. Estimate the probability of each event.
(The total probabilities must add up to 1.)5. Select the decision rule to evaluate the
alternatives.
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Decision Rules
Decision Making Under Uncertainty is when you are unable to estimate the probabilities of events. Maximin: The best of the worst. A pessimistic approach. Maximax: The best of the best. An optimistic approach. Minimax Regret: Minimizing your regret (also pessimistic) Laplace: The alternative with the best weighted payoff
using assumed probabilities.
Decision Making Under Risk is when one is able to estimate the probabilities of the events. Expected Value: The alternative with the highest weighted
payoff using predicted probabilities.
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AlternativesAlternatives LowLow HighHigh
Small facilitySmall facility 200200 270270Large facilityLarge facility 160160 800800Do nothingDo nothing 00 00
EventsEvents(Uncertain Demand)(Uncertain Demand)
MaxiMin DecisionExample A.6 a.
1.1. Look at the payoffs for each alternative and identify the Look at the payoffs for each alternative and identify the lowest 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 800800Do nothingDo nothing 00 00
EventsEvents(Uncertain Demand)(Uncertain Demand)
MaxiMax Decision Example A.6 b.
1.1. Look at the payoffs for each alternative and identify the Look at the payoffs for each alternative and identify the ““highesthighest” 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.6 c.
AlternativesAlternatives LowLow HighHigh(0.5)(0.5) (0.5) (0.5)
Small facilitySmall facility 200200 270270Large facilityLarge facility 160160 800800Do nothingDo nothing 00 00
EventsEvents
200*0.5 + 270*0.5 = 235200*0.5 + 270*0.5 = 235160*0.5 + 800*0.5 = 480 160*0.5 + 800*0.5 = 480
Multiply each payoff by the probability of Multiply each payoff by the probability of occurrence 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.6 d.
AlternativesAlternatives LowLow HighHigh
Small facilitySmall facility 200200 270270Large facilityLarge facility 160160 800800Do nothingDo nothing 00 00
EventsEvents(Uncertain Demand)(Uncertain Demand)
Look at Look at eacheach payoff and ask yourself, payoff and ask yourself, “If I end up here, do “If I end up here, do I have any regrets?”I have any regrets?”
Your regret, if any, is the difference between that payoff Your regret, if any, is the difference between that payoff and what you could have had by choosing a different and 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 Regret Example A.6 d. continued
AlternativesAlternatives LowLow HighHigh
Small facilitySmall facility 200200 270270Large facilityLarge facility 160160 800800Do nothingDo nothing 00 00
EventsEvents(Uncertain Demand)(Uncertain Demand)
If you chose a small If you chose a small facility and demand is facility and demand is low, you have zero low, you have zero regret.regret.
If you chose a large facility and If you chose a large facility and demand is low, you have a regret of demand is low, you have a regret of 40. (The difference between the 40. (The difference between the 160 you got and the 200 you could 160 you got and the 200 you could have had.) have had.)
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MiniMax Regret Example A.6 d. continued
AlternativesAlternatives LowLow HighHigh
Small facilitySmall facility 200200 270270Large facilityLarge facility 160160 800800Do nothingDo nothing 00 00
EventsEvents(Uncertain Demand)(Uncertain Demand)
Alternatives LowAlternatives Low HighHigh
Small facility 0Small facility 0 530530Large facility 40Large facility 40 00Do nothing 200Do nothing 200 800800
EventsEvents
MaxRegret MaxRegret 530 530 40 40 800 800
Regret MatrixRegret Matrix
Building a large Building a large facility offers the facility offers the least regret.least regret.
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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 270270Large facilityLarge facility 160160 800800Do nothingDo nothing 00 00
EventsEvents
200*0.4 + 270*0.6 = 242200*0.4 + 270*0.6 = 242160*0.4 + 800*0.6 = 544 160*0.4 + 800*0.6 = 544
Multiply each payoff by the probability of Multiply each payoff by the probability of occurrence 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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Example A.7
Expected Value AnalysisExpected Value Analysis
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Application A.4
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Application A.4
840 – 840 = 0840 – 840 = 0
840 – 370 = 470840 – 370 = 470
840 – 25 = 830840 – 25 = 830
1150 – 440 = 7101150 – 440 = 710
1150 – 220 = 9301150 – 220 = 930
1150 – 1150 = 01150 – 1150 = 0 670 – (-25) = 695670 – (-25) = 695
670 – 670 = 0670 – 670 = 0
670 – 190 = 480670 – 190 = 480 710710
930930
830830
What is the minimax regret solution?What is the minimax regret solution?
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Application A.5
© 2007 Pearson Education
Decision TreesDecision Trees are schematic models are schematic models of alternatives available along with of alternatives available along with their possible consequences.their possible consequences.
They are used in sequential decision They are used in sequential decision situations.situations.
Decision points are represented by Decision points are represented by squares. squares.
Event points are represented by Event points are represented by circles.circles.
Decision TreesDecision Trees
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= Event node= Event node
= Decision node= Decision node
1st1stdecisiondecision
PossiblePossible2nd 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
EE 11 &
Pro
babili
ty
& Pro
babili
ty
Altern
ativ
e 1
Altern
ativ
e 1
Alternative 2
Alternative 2
Payoff 1Payoff 1
Payoff 2Payoff 2
1 2
Decision TreesDecision Trees
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Decision TreesDecision Trees
After drawing a decision tree, we solve it by working from right to left, starting with decisions farthest to the right, and calculating the expected payoff for each of its possible paths.
We pick the alternative for that decision that has the best expected payoff.
We “saw off,” or “prune,” the branches not chosen by marking two short lines through them.
The decision node’s expected payoff is the one associated with the single remaining branch.
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Smal
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Smal
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Large facility
Large facility
1
Drawing the TreeDrawing the TreeExample A.8Example A.8
© 2007 Pearson Education
Smal
l fac
ility
Smal
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ility
Large facility
Large facility
Low demand [0.4]Low demand [0.4]
Don’t expandDon’t expand
ExpandExpand
$200$200
$223$223
$270$270
High demand
High demand
[0.6][0.6]
1
2
Drawing the TreeDrawing the TreeExample A.8Example A.8 continuedcontinued
© 2007 Pearson Education
Smal
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Smal
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Large facility
Large facility
1
Low dem
and
Low dem
and
[0.4]
[0.4]
Low demand [0.4]Low demand [0.4]
Don’t expandDon’t 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
High demand
High demand
[0.6][0.6]
High demand [0.6]High demand [0.6]
2
3
Completed DrawingCompleted DrawingExample A.8Example A.8
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Solving Decision #3Solving Decision #3 Example A.8Example A.8
Low dem
and
Low dem
and
[0.4]
[0.4]
Smal
l fac
ility
Smal
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ility
Large facility
Large facility
Low demand [0.4]Low demand [0.4]
Don’t expandDon’t 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
High demand
High demand
[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
© 2007 Pearson Education
Don’t expandDon’t expand
ExpandExpand
Do nothingDo nothing
AdvertiseAdvertise
$200$200
$223$223
$270$270
$40$40
$800$800
$160$160Low d
emand
Low dem
and
[0.4]
[0.4]
Smal
l fac
ility
Smal
l fac
ility
Large facility
Large facility
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
High demand
High demand
[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
© 2007 Pearson Education
$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 a Expanding has a higher value.higher value.
Low dem
and
Low dem
and
[0.4]
[0.4]
$160$160
Smal
l fac
ility
Smal
l fac
ility
Large facility
Large facility
Low demand [0.4]Low demand [0.4]
Don’t expandDon’t expand
ExpandExpand
Do nothingDo nothing
AdvertiseAdvertise
$200$200
$223$223
$270$270
$40$40
$800$800
High demand
High demand
[0.6][0.6]
High demand [0.6]High demand [0.6]
1
2
3
$270$270
© 2007 Pearson Education
$470$470
x 0.4 = $80x 0.4 = $80
x 0.6 = $162x 0.6 = $162
$242$242
$160$160Low d
emand
Low dem
and
[0.4]
[0.4]
$270$270
$160$160
Smal
l fac
ility
Smal
l fac
ility
Large facility
Large facility
Low demand [0.4]Low demand [0.4]
Don’t expandDon’t 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
High demand
High demand
[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
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Solving Decision #1Solving Decision #1 Example A.8Example A.8
$242$242
$160$160Low d
emand
Low dem
and
[0.4]
[0.4]
$270$270
$160$160
Smal
l fac
ility
Smal
l fac
ility
Large facility
Large facility
Low demand [0.4]Low demand [0.4]
Don’t expandDon’t 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
High demand
High demand
[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
© 2007 Pearson Education
$160$160Low d
emand
Low dem
and
[0.4]
[0.4]
$270$270
$160$160
Smal
l fac
ility
Smal
l fac
ility
Large facility
Large facility
$242$242
$544$544
Low demand [0.4]Low demand [0.4]
Don’t expandDon’t 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
High demand
High demand
[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
© 2007 Pearson Education
Application A.6 Application A.6
OM Explorer Solution OM Explorer Solution
© 2007 Pearson Education
Solved Problem 1Solved Problem 1
250 –250 –
200 –200 –
150 –150 –
100 –100 –
50 –50 –
0 –0 –
Total revenuesTotal revenues
Total costsTotal costs
Units (in thousands)Units (in thousands)
Do
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Do
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|| || || || || || || ||
11 22 33 44 55 66 77 88
Break-evenBreak-evenquantityquantity
3.13.1
$77.7$77.7
© 2007 Pearson Education
Solved Problem 4Solved Problem 4
Bad times [0.3]Bad times [0.3]
Normal times [0.5]Normal times [0.5]
Good times [0.2]Good times [0.2]
One liftOne lift
Two liftsTwo lifts
Bad times [0.3]Bad times [0.3]
Normal times [0.5]Normal times [0.5]
Good times [0.2]Good times [0.2]
$256.0$256.0
$225.3$225.3
$256.0$256.0
$191$191
$240$240
$240$240
$151$151
$245$245
$441$441