cf_MAT540_w2_ch12_hwk1_template.xlsx

Q1

States of Nature Summary Decision

Decision Gasoline Availablity a) maximax Motel

Investment Shortage Stable Supply Surplus Maximum Minimum b) maximin Theater

Motel -$7,500 $12,000 $23,000 $23,000 -$7,500 c) minimax regret Motel or Restaurant

Restaurant $3,000 $7,000 $6,500 $7,000 $3,000 d) Hurwicz (alpha = 0.4) Theater

Theater $5,000 $6,000 $4,000 $6,000 $4,000 e) Equal Likelihood Motel

Maximax decision =

Maximin decision =

Regret Table

States of Nature

Decision Gasoline Availablity

Investment Shortage Stable Supply Surplus Maximum

Motel $12,500 $0 $0 $12,500

Restaurant $2,000 $5,000 $16,500 $16,500

Theater $0 $6,000 $19,000 $19,000

Minimax regret =

Hurwicz

alpha = 0.3 Decision:

1 – alpha = 0.7

Motel $1,650

Restaurant $4,200

Theater $4,600

Equal Likelihood

Motel $9,167 Decision:

Restaurant $5,500

Theater $5,000

Q2

Decision Tables

Data

Profit Rain Overcast Sunshine EV

Probability 0.35 0.25 0.4 Sun Visor

Sun Visors -400 -200 1500 Umbrella

Umbrellas 2100 0 -800

Opportunity Loss Table

Rain Overcast Sunshine EOL

Probability 0.35 0.25 0.4 Sun Visor

Sun Visors 2500 200 0 Umbrella

Umbrellas 0 0 2300

Decision:

Minimize your Expected Opportunity Loss

Q3

Real estate Development

Decision Tables

Interest Rate

Project Decline (0.45) Stable (0.35) Increase (0.2) EV

Office park $0.40 $1.55 $3.50 Office park Decision

Office building 2.5 1.8 2.75 Office building

Warehouse 1.7 1.45 1.5 Warehouse

Mall 0.8 2.3 3.7 Mall

Condominiums 3.2 1.5 0.5 Condominiums

Opportunity Loss table

Interest Rate

Project Decline (0.45) Stable (0.35) Increase (0.2)

Office park

Office building

Warehouse

Mall

Condominiums

EVPI

Q4

Economic Conditions

Degree Program Recession Average Good Robust Maximum Minimum Summary Decision

Graphic design 150,000 175,000 220,000 200,000 220,000 150,000 a) maximax Real estate

Nursing 160,000 180,000 205,000 215,000 215,000 160,000 b) maximin Nursing

Real estate 125,000 165,000 220,000 210,000 220,000 125,000 c) equal likelihood Real estate

Medical technology 135,000 180,000 210,000 270,000 270,000 135,000 d) Hurwicz (alpha = 0.5) Real estate

Culinary technology 110,000 145,000 235,000 205,000 235,000 110,000

Computer information technology 130,000 150,000 190,000 245,000 245,000 130,000

Maximax decision =

Maximin decision =

Regret Table

Economic Conditions

Degree Program Recession Average Good Robust MAX MIN

Graphic design 10,000 5,000 15,000 70,000

Nursing 0 0 30,000 55,000

Real estate 35,000 15,000 15,000 60,000

Medical technology 25,000 0 25,000 0

Culinary technology 50,000 35,000 0 65,000

Computer information technology 30,000 30,000 45,000 25,000

Decision: Maximax 0

Equal Likelihood Decision: Maximin 0

Graphic design $186,250

Nursing $190,000

Real estate $180,000

Medical technology $198,750

Culinary technology $173,750

Computer information technology $178,750 Decision:

Hurwicz

alpha = 0.4

1 – alpha = 0.6

Graphic design $178,000

Nursing $182,000

Real estate $163,000

Medical technology $189,000

Culinary technology $160,000

Computer information technology $176,000 Decision:

Q5

0.7

Shortage

250000 Problem #25 (reference)

Compact Cars 250000 Data Results

Profit Shortage Surplus EMV

0.3 Probability 0.7 0.3

Surplus Compact cars 250000 150000

150000 Full-sized cars -90000 650000

150000 Trucks 125000 180000

0.7

Shortage

-90000

Full-sized cars -90000

1

0 0.3

Surplus Decision

650000

650000

0.7

Shortage

125000

Trucks 125000

0.3

Surplus

180000

170000 180000

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