Mat 540: quantitative methods week 2 discussion, quiz and homework

In your own words, explain how to obtain the “expected value of perfect information” for any payoff table, which has probabilities associated with each state of nature. Then, provide an example, drawing from any of the payoff tables in Problems 1-17 in the back of Chapter 12. If no probabilities are given for the states of nature, then assume equal likelihood.

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

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 = 0.50)

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