SOLVED:Decision theory




MAT 540
Week 2 HomeworkChapter 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
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 (a = 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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Weather Conditions
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
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.
Interest Rate
Decline Stable Increase
Office park $0.4 $1.55 $3.5
Office building 2.5 1.8 2.75
Warehouse 1.7 1.45 1.5
Mall 0.8 2.3 3.5
Condominiums 3.2 1.5 0.5
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4. The director of career advising at Orange Community College wants to use decision analysis to
provide information to help students decide which 2-year degree program they should pursue. The
director has set up the following payoff table for six of the most popular and successful degree
programs at OCC that shows the estimated 5-Year gross income ($) 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
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 (a=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:
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Gasoline Availability
Compact cars $25,000 $150,000
Full-sized cars -90,000 650,000
Trucks 125,000 170,000
Decision Tree diagram to complete:
Compact cars
Full-sized cars
Shortage 0.7