Posted: February 6th, 2022
MAT540
Week 2 Homework
Chapter 12
8. 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
16. 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.
24. In Problem 13 the PlacePlus 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.
Reference Problem 13: PlacePlus, 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 5year financial return (in $1,000,000s) given that interest rates will decline, remain stable, or increase, are shown in the following payoff table:


Interest Rate 

Project 
Decline 
Stable 
Increase 
Office park 
$0.5 
$1.7 
$4.5 
Office building 
1.5 
1.9 
2.5 
Warehouse 
1.7 
1.4 
1.0 
Mall 
0.7 
2.4 
3.6 
Condominiums 
3.2 
1.5 
0.6 
32. The director of career advising at Orange Community College wants to use decision analysis to provide information to help students decide which 2year degree program they should pursue. The director has set up the following payoff table for six of the most popular and successful degree programs at OCC that shows the estimated 5year gross income ($) 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 likelihood
d. Hurwicz (α = 0.50)
36. Construct a decision tree for the decision situation described in Problem 25 and indicate the best decision.
Reference Problem 25: Fenton and Farrah Friendly, husbandandwife 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 fullsized 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 
Fullsized cars 
100,000 
600,000 
Trucks 
120,000 
170,000 
Decision Tree diagram to complete:
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