MAT540
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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 (? = 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 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.
Reference Problem 13: 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:
Interest Rate
Project
Decline
Stable
Increase
Office park
$0.5
$1.7
$4.5
Office building
1.5
1.9
2.5
Warehouse
1.7
1.4
1.0
Mall
0.7
2.4
3.6
Condominiums
3.2
1.5
0.6
32. The
director of career advising at Orange Community College wants to use decision
analysis to provide information to help students decide which 2-year degree
program they should pursue. The director has set up the following payoff table
for six of the most popular and successful degree programs at OCC that shows
the estimated 5-year gross income ($) 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
Determine the best degree program in terms of projected income, using the
following decision criteria:
a.
Maximax
b.
Maximin
c.
Equal likelihood
d.
Hurwicz (? = 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, 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
Decision Tree diagram to complete:
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