Discuss the following:
Q1. 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 five years. The various development projects and their five-year financial return ($ millions) given that interest rates will decline, remain stable, or increase are shown in the following payoff table
Interest Rates
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
Determine the best investment using the following decision criteria.
- Maximax
- Maximin
- Equal likelihood
- Hurwicz (x=.3)
Q2. The Oakland Bombers professional basketball team just missed making the playoffs last season and believes it needs to sign only one very good free agent to make the playoffs next season. The team is considering four players: Barry Byrd, Rayneal O' Neil, Marvin Johnson, and Michael Gordan. Each player differs according to position, ability, and attractiveness to fans. The payoffs (in $ millions) to the team for each player based on the contract, profits from attendance, and team product sales for several different seasonal outcomes are provided in the following table.
Season Outcome
Player Loser Competitive Make Playoffs
Byrd $-3.2 $1.3 4.4
O'Neil -5.1 1.8 6.3
Johnson -2.7 0.7 5.8
Gordan -6.3 -1.6 9.6
Determine the best decision using the following decision criteria.
- Maximax
- Maximin
- Hurwicz (x=.60)
- Equal likelihood
Q3. Construct a decision tree for the decision situated below 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 show in the following payoff table. Determine which type of dealership the couple should purchase.
Gasoline Availability
Dealership Shortage .6 Surplus .4
Compact cars $300,000 $150,000
Full-sized cars -100,000 600,000
Trucks 120,000 170,000
Q4. The management of first American Bank was concerned about the potential loss that might occur in the event of a physical catastrophe such as a power failure or a fire. The bank estimated that the loss from one of these incidents could be as much a $100 million, including losses due to interrupted service and customer relations. One project the bank is considering is the installation of an emergency power generator at its operations headquarters. The cost of the emergency generator is $800,000, and if it is installed no losses from this type of incident will be incurred. However, if the generator is not installed, there is a 10% chance that a power outage will occur during the next year. If there is an outage, there is a .05 probability that the resulting losses will be very large, or approximately $80 million in lost earnings. Alternatively, it is estimated that there is a .95 probability of only slight losses of around $1 million. Using decision tree analysis, determine whether the bank should install the new power generator.