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36) A company that is introducing a new product has to choose between four different manufacturing
methods, referred to as methods A, B, C and D. Depending on the demand for the product, they have
forecasted different levels of expenses for the year (values are in thousands). The company has identified
three possible states of nature for economic growth, and named them High, Medium, and Low. Which
alternative is best in accordance with an optimistic outlook? Which alternative is best according to a
pessimist?
High
Medium
Low
Method A
$450
$670
$780
Method B
$950
$320
$200
Method C
$375
$575
$775
Method D
$800
$400
$300
1) The first choice in a decision tree is the leftmost decision node.
2) The average probability, P(E), for all branches leaving an event node is 1/n, where n is the number of
branches leaving that event node.
3) The online courses were already beginning to pay off, Josie thought as she sketched out her first
decision tree. All payoffs are in positive dollars and she was confident her estimates were accurate.
Clearly, the best choice for her was to choose High Demand.
4) When using decision tree analysis:
A) the sum of the expected payoffs must always equal zero.
B) round nodes represent decision points.
C) there must be more square nodes than round nodes.
D) probabilities for all branches leaving a chance node must sum to 1.0.
5) In order for a decision tree to be a valuable decision tool, the decision-maker should be in a condition
of:
A) certainty.
B) risk.
C) uncertainty.
D) equilibrium.
6) An operations manager has developed this decision tree to evaluate the alternatives for a planned
expansion. If the probability of high demand is 0.6, what is the best course of action?
A) Alternative A
B) Alternative B
C) Alternative C
D) Alternative D
7) A marketing director must decide among four alternatives for a new marketing campaign. She
ascertains that the probability of high demand is 0.8 and the probability of low demand is 0.2. What is the
best choice with the payoffs shown in the tree?
A) Alternative A
B) Alternative B
C) Alternative C
D) Alternative D
8) A marketing director must decide among four alternatives for a new marketing campaign. She
ascertains that the probability of high demand is 0.45 and the probability of low demand is 0.55. What is
the best choice with the payoffs shown in the tree?
A) Alternative A
B) Alternative B
C) Alternative C
D) Alternative D
9) George Burdell must decide among four alternatives for an oil exploration project. He estimates that
the probability of high demand is 0.3 and the probability of low demand is 0.7. What is the best choice
with the payoffs shown in the tree?
A) Alternative A
B) Alternative B
C) Alternative C
D) Alternative D
10) Analyze the following decision tree. Determine the missing probabilities, and identify the alternative
that maximizes the expected payoff.
A) Option 1, with an expected payoff of less than $25
B) Option 1, with an expected payoff of $25 or more
C) Option 2, with an expected payoff of less than $25
D) Option 2, with an expected payoff of $25 or more
11) Analyze the following decision tree. After determining the missing probabilities, identify which
alternative (Option 1 or Option 2) has the higher expected payoff. What is the expected payoff?
A) Option 1, with an expected payoff of less than $25
B) Option 1, with an expected payoff of $25 or more
C) Option 2, with an expected payoff of less than $25
D) Option 2, with an expected payoff of $25 or more
12) Analyze the following decision tree. After determining the missing probabilities, identify which
alternative (Option 1 or Option 2) has the higher expected payoff. What is the expected payoff?
A) Option 1, with an expected payoff of less than $35
B) Option 1, with an expected payoff of no less than $35
C) Option 2, with an expected payoff of less than $35
D) Option 2, with an expected payoff of more than $35
13) A(n) ________ is a schematic model of alternatives available to the decision maker, along with their
possible consequences.
14) The ________ nodes have probabilities associated with them in a decision tree.
15) Decision trees are typically used in the situation of decision making under ________.
16) A chance event that has an impact on the outcome of the choice but is not under the manager's control
is called a(n) ________.
17) Under what conditions can decision trees be useful?
45
18) A new minor league baseball team is coming to town and the owners have decided to build a new
stadium, either small or large. The success of the team with regard to ticket sales will be either high or
low with probabilities of 0.75 and 0.25, respectively. If demand for tickets is high, the large stadium
would provide a payoff of approximately $20 million. If ticket sales are low, the loss on the large stadium
would be $5 million. If a small stadium is constructed, and ticket sales are low, the payoff is $500,000 after
deducting the cost of construction. If ticket sales are high, the team can choose to build an upper deck, or
to maintain the existing facility. Expanding the stadium in this scenario has a payoff of $10 million,
whereas maintaining the same number of seats has a payoff of only $3 million.
a. Draw a decision tree for this problem.
b. What should management do to achieve the highest expected payoff?
Answer:
46
19) The Hill O'Beans Coffee Company operates a chain of coffee shops downtown and has decided to
open a new store. The demand will be weak, fair, or strong; probabilities are 0.25, 0.30, and 0.45,
respectively.
If the company installs a small booth that sells only coffee, the associated payoffs are -$25,000; 25,000; and
$100,000 for weak, fair, and strong demand. If the company chooses an expanded facility that offers
sandwiches and breakfast foods, it must build a kitchen and rent additional space. The payoffs for an
expanded facility are -$200,000, -$25,000, and $500,000.
a. Draw a decision tree for this problem.
b. What should management do to achieve the highest expected payoff?
Answer:
47
20) Keith Monroe is deciding among four alternatives and fleshes out the decision tree shown below. He
has developed excellent estimates of payoffs but admits he has no clue about the probabilities for the two
states of nature. He wants to cover all of his bases, so he would like to calculate the probability of high
demand for which each alternative is superior. Analyze this situation and make recommendations for
him. He promises to cut you in for 30% of the profits if you can show him how to calculate the ranges.
Answer: Approaches to this problem may vary. The value for each alternative is given by this set of
equations:
48
The graph shows that Alternative D is initially superior, giving way to Alternative C, which yields to
Alternative A, which is supplanted by Alternative B as the probability of high demand increases from 0
to 1. These three intersections on the graph can be determined by setting up three sets of simultaneous
equations.
D & C
VD = -600pHIGH + 900 = 650 = VC
-600pHIGH = -250
pHIGH = .41
