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

Restaurant            3,000                  7,000                         6,500

Theater                 5,000                   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:

Weather Conditions

Decision              Rain            Overcast              Sunshine

.35             .25                         .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 building 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 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 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

Project                          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

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

information technology

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:

Gasoline Availability

Dealership          Shortage              Surplus

.6                         .4

Compact cars     \$ 250,000             \$150,000

Full-sized cars   -90,000                   650,000

Trucks                 125,000                   170,000

Decision Tree diagram to complete:  (Please see below)

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