Help with Optimization and Decision Support Modeling for Business HW4

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M7_PracticeProblems_Ch9_Solution.xlsx
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Prob1

40%
2500
2500 2500
0 580 60%
20%
-700
2 -700 -700
0 900
900
0 820 900 900
80%
1 800
820 800 800
750
750 750

Prob2a

Payoff Table ($thousands) Expected
State of Nature Payoff
Alternative S1 S2 S3 ($thousands)
A1 -100 10 100 33
A2 -10 20 50 29
A3 10 10 60 35
Prior Probability 0.2 0.3 0.5

Prob3b

Payoff Table State of Nature Expected
Alternative p = 0.05 p = 0.25 Payoff
Screen -$1,500 -$1,500 -$1,500
Don't Screen -$750 -$3,750 -$1,350
Prior Probability 0.8 0.2

Prob3d

Template for Posterior Probabilities
Data: P(Finding | State)
State of Prior Finding
Nature Probability Defective Nondefective
p = 0.05 0.8 0.05 0.95
p = 0.25 0.2 0.25 0.75
Posterior P(State | Finding)
Probabilities: State of Nature
Finding P(Finding) p = 0.05 p = 0.25
Defective 0.09 0.444 0.556
Nondefective 0.91 0.835 0.165

Prob3e

44.4%
p=0.05
-1625
Screen -1500 -1625
0 -1625 55.6%
p=0.25
9% -1625
Defective -1500 -1625
1
0 -1625 44.4%
p=0.05
-875
Don't Screen -750 -875
0 -2541.6666666667 55.6%
p=0.25
-3875
Pre-screen -3750 -3875
-125 -1392.95 83.5%
p=0.05
-1625
Screen -1500 -1625
0 -1625 16.5%
p=0.25
91% -1625
Nondefective -1500 -1625
2
0 -1370 83.5%
p=0.05
-875
Don't Screen -750 -875
2
-1350 0 -1370 16.5%
p=0.25
-3875
-3750 -3875
80%
p=0.05
-1500
Screen -1500 -1500
0 -1500 20%
p=0.25
-1500
Don't Pre-screen -1500 -1500
2
0 -1350 80%
p=0.05
-750
Don't Screen -750 -750
0 -1350 20%
p=0.25
-3750
-3750 -3750

Prob4d

Template for Posterior Probabilities
Data: P(Finding | State)
State of Prior Finding
Nature Probability Predict Sell 10,000 Predict Sell 100,000
Sell 10,000 0.5 0.667 0.333
Sell 100,000 0.5 0.333 0.667
Posterior P(State | Finding)
Probabilities: State of Nature
Finding P(Finding) Sell 10,000 Sell 100,000
Predict Sell 10,000 0.5 0.667 0.333
Predict Sell 100,000 0.5 0.333 0.667

Prob5a

Payoff Table State of Nature Expected
Alternative S1 S2 Payoff
A1 $400 -$100 $100
A1 $0 $100 $60
Prior Probability 0.4 0.6

Prob5d

Alternative 1
40% 400
State 1 400 400
1
0 400
Alternative 2
0
0 0%
220
Alternative 1
60% -100
State 2 -100 -100
2
0 100
Alternative 2
100
100 100

Prob5f

Template for Posterior Probabilities
Data: P(Finding | State)
State of Prior Finding
Nature Probability Predict S1 Predict S2
Actual S1 0.4 0.6 0.4
Actual S2 0.6 0.2 0.8
Posterior P(State | Finding)
Probabilities: State of Nature
Finding P(Finding) Actual S1 Actual S2
Predict S1 0.36 0.667 0.333
Predict S2 0.64 0.250 0.750

Prob5g

Payoff Table State of Nature Expected
Alternative S1 S2 Payoff
A1 $400 -$100 $233.33
A1 $0 $100 $33.33
Prior Probability 0.6667 0.3333

Prob5h

Payoff Table State of Nature Expected
Alternative S1 S2 Payoff
A1 $400 -$100 $25
A1 $0 $100 $75
Prior Probability 0.25 0.75

Prob5k

66.7%
S1 Occurs
300
Choose A1 400 300
0 133.3333333333 33.3%
S2 Occurs
36% -200
Predict S1 -100 -200
1
0 133.3333333333 66.7%
S1 Occurs
-100
Choose A2 0 -100
0 -66.6666666667 33.3%
S2 Occurs
0
Research 100 0
-100 32 25%
S1 Occurs
300
Choose A1 400 300
0 -75 75%
S2 Occurs
64% -200
Predict S2 -100 -200
2
0 -25 25%
S1 Occurs
-100
Choose A2 0 -100
2
100 0 -25 75%
S2 Occurs
0
100 0
40%
S1 Occurs
400
Choose A1 400 400
0 100 60%
S2 Occurs
-100
No Research -100 -100
1
0 100 40%
S1 Occurs
0
Choose A2 0 0
0 60 60%
S2 Occurs
100
100 100