MAT 540 Week 2 (A++++++++++++++++++Grade) New Data of Jan . 2015

MAT540 Homework

Week 2

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MAT540

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:

Gasoline Availability

Investment Shortage Stable Supply Surplus

Motel $-8,000 $15,000 $20,000

Restaurant 2,000 8,000 6,000

Theater 6,000 6,000 5,000

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 30% chance of rain, a 15% chance of overcast skies,

and a 55% 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:

Weather Conditions

Decision Rain Overcast Sunshine

.30 .15 .55

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

Umbrellas 2,000 0 -900

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 building and selling MAT540 Homework

Week 2

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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 shown 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 .50 probability that interest rates will decline, a .40 probability that rates will remain

stable, and a .10 probability that rates will increase.

a. Using expected value, determine the best project.

b. Determine the expected value of perfect information.

Interest Rate

Project Decline Stable Increase

Office park $0.5 $1.7 $4.5

Office building 1.5 1.9 2.5

Warehouse 1.7 1.4 1.0

Mall 0.7 2.4 3.6

Condominiums 3.2 1.5 0.6

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:

Economic Conditions

Degree Program Recession Average Good Robust

Graphic design 145,000 175,000 220,000 260,000

Nursing 150,000 180,000 205,000 215,000

Real estate 115,000 165,000 220,000 320,000

Medical technology 130,000 180,000 210,000 280,000

Culinary technology 115,000 145,000 235,000 305,000

Computer information

technology 125,000 150,000 190,000 250,000

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

criteria:

a. Maximax

b. Maximin

c. Equal likelihoodMAT540 Homework

Week 2

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d. Hurwicz (α = 0.50)

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:

Gasoline Availability

Dealership Shortage Surplus

.6 .4

Compact cars $ 300,000 $150,000

Full-sized cars -100,000 600,000

Trucks 120,000 170,000

Decision Tree diagram to complete: