MAT 540 Homework Week 2

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Q1

States of Nature Summary Decision
Decision Gasoline Availablity a) maximax Motel
Investment Shortage Stable Supply Surplus Maximum Minimum b) maximin Theater
Motel -$8,000 $15,000 $20,000 $20,000 -$8,000 c) minimax regret Motel or Restaurant
Restaurant $2,000 $8,000 $6,000 $8,000 $2,000 d) Hurwicz (alpha = 0.4) Theater
Theater $6,000 $6,000 $5,000 $6,000 $5,000 e) Equal Likelihood Motel
Maximax decision =
Maximin decision =
Regret Table
States of Nature
Decision Gasoline Availablity
Investment Shortage Stable Supply Surplus Maximum
Motel $14,000 $0 $0 $14,000
Restaurant $4,000 $7,000 $14,000 $14,000
Theater $0 $9,000 $15,000 $15,000
Minimax regret =
Hurwicz
alpha = 0.4 Decision:
1 - alpha = 0.6
Motel $3,200
Restaurant $4,400
Theater $5,400
Equal Likelihood
Motel $9,000 Decision:
Restaurant $5,333
Theater $5,667

Q2

Problem 16 - Concessions
Decision Tables
Data
Profit Rain Overcast Sunshine EV
Probability 0.3 0.15 0.55 Sun Visor Best one
Sun Visors -500 -200 1500 Umbrella
Umbrellas 2000 0 -900
Opportunity Loss Table
Rain Overcast Sunshine EOL
Probability 0.3 0.15 0.55 Sun Visor
Sun Visors 2500 200 0 Umbrella
Umbrellas 0 0 2400
Decision:
Minimize your Expected Opportunity Loss

Q3

Problem 24 - Real estate Development
Decision Tables
Interest Rate
Project Decline (0.5) Stable (0.4) Increase (0.1) EV
Office park $0.50 $1.70 $4.50 Office park $1.38 Decision Condominium
Office building 1.5 1.9 2.5 Office building $1.76
Warehouse 1.7 1.4 1 Warehouse $1.51
Mall 0.7 2.4 3.6 Mall $1.67
Condominiums 3.2 1.5 0.6 Condominiums $2.26
Opportunity Loss table
Interest Rate
Project Decline (0.5) Stable (0.4) Increase (0.1)
Office park $2.70 $0.70 $0.00 $1.63
Office building $1.70 $0.50 $2.00 $1.25
Warehouse $1.50 $1.00 $3.50 $1.50
Mall $2.50 $0.00 $0.90 $1.34
Condominiums $0.00 $0.90 $3.90 $0.75
EVPI (= EOL)
Altervatively, the above answer can be obtained by
EV with perfect information EV without perfect information EVPI
$3.01 $0.00

Q4

Economic Conditions
Degree Program Recession Average Good Robust Maximum Minimum Summary Decision
Graphic design 145,000 175,000 220,000 260,000 260,000 145,000 a) maximax Real estate
Nursing 150,000 180,000 205,000 215,000 215,000 150,000 b) maximin Nursing
Real estate 115,000 165,000 220,000 320,000 320,000 115,000 c) equal likelihood Real estate
Medical technology 130,000 180,000 210,000 280,000 280,000 130,000 d) Hurwicz (alpha = 0.5) Real estate
Culinary technology 115,000 145,000 235,000 305,000 305,000 115,000
Computer information technology 125,000 150,000 190,000 250,000 250,000 125,000
Maximax decision =
Maximin decision =
Equal Likelihood
Graphic design
Nursing
Real estate
Medical technology
Culinary technology
Computer information technology Decision:
Hurwicz
alpha = 0.5
1 - alpha = 0.5
Graphic design
Nursing Decision:
Real estate
Medical technology
Culinary technology
Computer information technology

Q5

0.6
Shortage
300000
Compact Cars 300000 Data Results
Profit Shortage Surplus EMV
0.4 Probability 0.6 0.4
Surplus Compact cars 300000 150000 240000
150000 Full-sized cars -100000 600000 180000
150000 Trucks 120000 170000 140000
0.6
Shortage
-100000
Full-sized cars -100000
1
0.4
Surplus Decision
600000
600000
0.6
Shortage
120000
Trucks 120000
0.4
Surplus
170000
170000 170000
ID Name Value Prob Pred Kind NS S1 S2 S3 S4 S5 Row Col Mark
0 TreePlan 0 0 0 D 3 1 2 3 0 0 14 1 TRUE
1 0 0 E 2 4 5 0 0 0 4 5 TRUE
2 0 0 E 2 6 7 0 0 0 14 5 TRUE
3 0 0 E 2 8 9 0 0 0 24 5 TRUE
4 1 T 0 0 0 0 0 0 2 9 TRUE
5 1 T 0 0 0 0 0 0 7 9 TRUE
6 2 T 0 0 0 0 0 0 12 9 TRUE
7 2 T 0 0 0 0 0 0 17 9 TRUE
8 3 T 0 0 0 0 0 0 22 9 TRUE
9 3 T 0 0 0 0 0 0 27 9 TRUE