week2 MAT 540 strayer uni Quantitative Methods –

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 MAT540 Homework Week 2 Page 1 of 3 

 

 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 

   

 

 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 Page 2 of 3 

 

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 

   

 

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 

 

 

   
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