Quantitative Methods:

I have 5 discussion problems that I need done. Attached is the 5 problems and the template to show the work

MAT540Homework

Week

2

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4

MAT54

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Week 2 Homework

Chapter 12

1. A local real estate investor in Orlando is considering three alternative investments; a motel, a

restaurant, or a theater. Profits from the motel or restaurant will be affected by the availability of

gasoline and the number of tourists; profits from the theater will be relatively stable under any

conditions. The following payoff table shows the profit or loss that could result from each

investment:

Investment

Weather Conditions

Shortage Stable Supply Surplus

Motel $-7,500 $12,000 $23,000

Restaurant 3000 7,000 6,500

Theater 5000 6,000 4,000

Determine the best investment, using the following decision criteria.

a. Maximax

b. Maximin

c. Minimax regret

d. Hurwicz (α = 0.4)

e. Equal likelihood

2. A concessions manager at the Tech versus A&M football game must decide whether to have the

vendors sell sun visors or umbrellas. There is a 35% chance of rain, a 25% chance of overcast skies,

and a 40% chance of sunshine, according to the weather forecast in college junction, where the

game is to be held. The manager estimates that the following profits will result from each decision,

given each set of weather conditions:

MAT540 Homework
Week 2

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Decision

Weather Conditions

Rain

0.35

Overcast

0.25

Sunshine

0.40

Sun visors $-400 $-200 $1,500

Umbrellas 2,100 0 -800

a. Compute the expected value for each decision and select the best one.

b. Develop the opportunity loss table and compute the expected opportunity loss for each

decision.

3. Place-Plus, a real estate development firm, is considering several alternative development projects.

These include building and leasing an office park, purchasing a parcel of land and building an

office building to rent, buying and leasing a warehouse, building a strip mall, and selling

condominiums. The financial success of these projects depends on interest rate movement in the

next 5 years. The various development projects and their 5- year financial return (in $1,000,000s)

given that interest rates will decline, remain stable, or increase, are in the following payoff table.

Place-Plus real estate development firm has hired an economist to assign a probability to each

direction interest rates may take over the next 5 years. The economist has determined that there is a

0.45 probability that interest rates will decline, a 0.35 probability that rates will remain stable, and a

0.2 probability that rates will increase.

a. Using expected value, determine the best project.

b. Determine the expected value of perfect information.

Project
Interest Rate

Decline Stable Increase

Office park $0.4 $1.55 $3.5

Office building 2.5 1.8 2.75

Warehouse 1.7 1.45 1.5

Mall 0.8 2.3 3.5

Condominiums 3.2 1.5 0.5

MAT540 Homework
Week 2

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4. The director of career advising at Orange Community College wants to use decision analysis to

provide information to help students decide which 2-year degree program they should pursue. The

director has set up the following payoff table for six of the most popular and successful degree

programs at OCC that shows the estimated 5-Year gross income ($) from each degree for four

future economic conditions:

Degree Program
Economic Conditions

Recession Average Good Robust

Graphic design 150,000 175,000 220,000 200,000

Nursing 160,000 180,000 205,000 215,000

Real estate 125,000 165,000 220,000 210,000

Medical technology 135,000 180,000 210,000 270,000

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

Computer information

technology

130,000 150,000 190,000 245,000

Determine the best degree program in terms of projected income, using the following decision criteria:

a. Maximax

b. Maximin

c. Equal likelihood

d. Hurwicz (α=0.4)

5. Construct a decision tree for the following decision situation and indicate the best decision.

Fenton and Farrah Friendly, husband-and-wife car dealers, are soon going to open a new dealership.

They have three offers: from a foreign compact car company, from a U.S. producer of full-sized

cars, and from a truck company. The success of each type of dealership will depend on how much

gasoline is going to be available during the next few years. The profit from each type of dealership,

given the availability of gas, is shown in the following payoff table:

MAT540 Homework
Week 2

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Dealership

Gasoline Availability

Shortage

0.7

Surplus

0.

3

Compact cars $25,000 $150,000

Full-sized cars -90,000 650,000

Trucks 125,000 170,000

Decision Tree diagram to complete:

1

2
3
4

Compact cars

Full-sized cars

Trucks

Shortage 0.7

Surplus 0.3

Shortage 0.7
Surplus 0.3
Surplus 0.3
Shortage 0.7

$250,000

$150,00

0

-$90,000

$650,000

$125,000

$170,000

2

>Q

1

of Nature

ecision

Decision

heater

Motel

,

0

,000

,000

$23,000 -$7,500

Restaurant

,500

$7,000 $3,000

(

)

Theater

Theater

$6,000 $4,000

qual Likelihood

Motel

decision =

decision =

States of Nature
Decision Gasoline Availablity
Investment Shortage Stable Supply Surplus Maximum
Motel

$0 $12,500

Restaurant

$5,000

$16,500

Theater $0 $6,000

,000

$19,000

Hurwicz
alpha =

Motel

Restaurant

Theater

Equal Likelihood
Motel

Decision:

Restaurant

Theater $5,000

																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																									States			Summary							D
	Gasoline Availablity		a) maximax						Motel
	Investment						Shortage		Stable Supply						Surplus			Maximum		Minimum		b) maximin												T
	-$			7					5																																																																					0	$	12		$2					3	c) minimax regret	Motel or				Restaurant
	$3,000		$7,000	$		6	d)		Hurwicz		alpha =			0.			4
		$	5,000			$6,000		$4,000	e)					E
		Maximax
		Maximin
	Regret Table
	$12,500			$0
$2,000		$16,500
	$1								9
Minimax regret =
				0.3							Decision:
	1 – alpha =					0.7
$1,650
$4,	200
$4,600
$9,167
$5,500

Q2

ability

0.4

0

00

Rain Overcast Sunshine

Probability 0.35 0.25 0.4 Sun Visor

Sun Visors

200 0 Umbrella

Umbrellas 0 0

Decision:

	Decision Tables
	Data
	Profit		Rain		Overcast		Sunshine		EV
			Prob		0.35		0.25		Sun Visor
	Sun Visors	-400	-200	1500		Umbrella
	Umbrellas	2100	–		8
Opportunity Loss Table
EOL
2500
2300
Minimize your Expected Opportunity Loss

Q3

Development

Decision Tables

EV

5

Office park Decision

Office building

1.5

Warehouse
Mall

1.5

Condominiums

Interest Rate

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

Office building
Warehouse
Mall
Condominiums

							Real estate
	Interest Rate
	Project		Decline (0.45)		Stable (0.35)		Increase (0.2)
		Office park	$0.40	$		1.5	$3.50
		Office building	2.5	1.8	2.75
		Warehouse	1.7	1.45
		Mall	0.8	2.3	3.7
		Condominiums	3.2	0.5
Opportunity Loss table
EVPI

Q4

Maximum Minimum Summary Decision

5,000

0,000

220,000 150,000 a) maximax Real estate

215,000 160,000 b) maximin Nursing

Real estate

220,000

220,000 125,000

Real estate

180,000 210,000

0,000 135,000

Real estate

205,000 235,000 110,000

150,000

5,000

245,000 130,000

Maximax decision =
Maximin decision =
Regret Table
Economic Conditions

Degree Program Recession Average Good Robust

Graphic design 10,000 5,000 15,000 70,000
Nursing 0 0 30,000

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

Nursing

Real estate

Medical technology

Culinary technology

Computer information technology

Decision:

Hurwicz

alpha = 0.4
1 – alpha =

Graphic design

Nursing

Real estate

Medical technology

Culinary technology

Computer information technology

Decision:

	Economic Conditions
	Degree Program		Recession		Average		Good		Robust
			Graphic design			1	50,000		17					22	200,000
				Nursing		1	60,000		180,000		205,000		2			15,000
	1			25,000	1	65,000		2	10,000	c) equal likelihood
			Medical technology		1		35,000		2	70,000	27	d) Hurwicz (alpha = 0.5)
			Culinary technology		110,000	1	45,000		235,000
			Computer information technology		1			30,000	190,000			24
MAX	MIN
55,000
$186,250
$190,000
$180,000
$198,750
$173,750
$178,750
0.6
$178,000
$182,000
$163,000
$189,000
$160,000
$176,000

Q5

0.7
Shortage

250000 Data

Profit Shortage Surplus

0.3 Probability 0.7 0.3
Surplus

250000

150000

150000

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

180000

Prob

0

0 0 0 D 3 1 2 3 0 0

1

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

250000

Problem #25 (reference)

Compact Cars

Results

EMV

Compact cars

150000

Full-sized cars

-90000

650000

Trucks

125000

180000

170000

ID

Name

Value

Pred

Kind

NS

S1

S2

S3

S4

S5

Row

Col

Mark

TreePlan

14

TRUE