Question

Problem 13-01 (Algorithmic) The following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature: State of Nature Decision Alternative S1 S2 S3 d1 260 140 100 d2 170 130 50 Choose the correct decision tree for this problem. (i) d2d1s3s2s1s3s2s1 (ii) d2d1s3s3s2s2s1s1 (iii) s3s2s1d2d1d2d1d2d1 (iv) d2d1s3s2s1s3s2s1 If the decision maker knows nothing about the probabilities of the three states of nature, what is the recommended decision using the optimistic, conservative, and minimax regret approaches? Optimistic approach Conservative approach Minimax regret approach

Answer #1

Problem 13-14 (Algorithmic) The following profit payoff table
shows profit for a decision analysis problem with two decision
alternatives and three states of nature: State of Nature Decision
Alternative S1 S2 S3 d1 250 100 100 d2 200 100 150 The
probabilities for the states of nature are P(s1) = 0.45, P(s2) =
0.25 and P(s3) = 0.3. What is the optimal decision strategy if
perfect information were available? S1 : S2 : S3 : What is the
expected value...

The following payoff table shows a profit for a decision
analysis problem with two decision alternatives and three states of
nature. In order to get full credit, show your all work done step
by step including cell calculations using excel functions.
State of Nature
Decion Alternatives
s1
s2
s3
d1
250
100
50
d2
100
75
100
a) Construct a decision tree for this problem.
b) Suppose that the decision-maker obtains the probabilities
P(s1)=0.65, P(s2)=0.15, and P(s3)=0.20.
Use the expected...

Problem 13-29 (Algorithmic) Three decision makers have assessed
utilities for the following decision problem (payoff in dollars):
State of Nature Decision Alternative S1 S2 S3 d1 30 50 -30 d2 80
110 -100 The indifference probabilities are as follows:
Indifference Probability (p) Payoff Decision maker A Decision maker
B Decision maker C 110 1.00 1.00 1.00 80 0.95 0.80 0.85 50 0.85
0.70 0.75 30 0.75 0.55 0.60 -30 0.60 0.25 0.50 -100 0.00 0.00 0.00
Find a recommended decision...

Consider the following Profit Payoff Table:
State of Nature
Decision Alternative
S1
S2
S3
d1
250
100
25
d2
100
100
75
The probabilities for the states of nature are
P(S1) = 0.65,
P(S2) = 0.15, and
P(S3) = 0.20.
What is the optimal decision strategy if perfect information
were available?
What is the expected value for the decision strategy developed
in part (a)?
Using the expected value approach, what is the recommended
decision without perfect information? What is its...

Q.1 Payoff Table: Choices: D1, D2, D3. States of Nature: S1, S2,
S3. Profit( in millions) for each of the States of Nature are given
below: For D1: $100, $400, $500. For D2:-$100, $500, $900. For D3:
-$200, $500, $1600. P(s1)=0.4, P(s2)=0.4, P(s3)=0.2. Sample
Information Data: Market Research Firm provides following data:
conditional probabilities: P(Fav/s1)= 0.40, P(Fav/s2)= 0.5,
P(Fav/s3)= 0.9. Then P(Fav)= .54
For the data given in Q.1, compute revised probabilities, draw
the decision tree, and enter the payoff...

Suppose a decision maker is considering three decision
alternatives: A1, A2, and A3. Three potential states of nature have
been identified: S1, S2, and S3. The payoff for each combination of
alternative and state of nature has been estimated and appears in
the following payoff table:
S1
S2
S3
A1
113
96
-65
A2
117
62
-52
A3
32
45
40
Calculate the regret (or opportunity loss) value for the
combination of A2 and S2.

Below is a payoff table involving three states of nature and
three decision alternatives. Decision States of Nature Alternative
s1 s2 s3 A –20 10 15 B 16 –5 8 C 15 25 –10 The probability of
occurrence of s1 is .2, and the probability of occurrence of s2 is
.3. The expected value of alternative C is _____.

Problem 4-11
(Algorithmic)
Following is the
payoff table for the Pittsburgh Development Corporation (PDC)
Condominium Project. Amounts are in millions of dollars.
State of
Nature
Decision Alternative
Strong Demand
S1
Weak Demand
S2
Small complex, d1
7
6
Medium complex, d2
12
6
Large complex, d3
19
-9
Suppose PDC is
optimistic about the potential for the luxury high-rise condominium
complex and that this optimism leads to an initial subjective
probability assessment of 0.8 that demand will be strong
(S1)...

The following payoff table shows profits for two decision
alternatives under three different states of nature. It is known
that the probability of the occurrence of state of nature 1 is 0.1.
Profit State of Nature 1 State of Nature 2 State of Nature 3
Decision Alternative 1 10 13 9 Decision Alternative 2 15 9 10 [4]
What should the probabilities of states of nature 2 and 3 be so
that the expected values of the two decision alternatives...

The following payoff table shows profits for two
decision alternatives under three different states of nature. It is
known that the probability of the occurrence of state of nature 1
is 0.1.
Profit
State of Nature 1
State of Nature 2
State of Nature 3
Decision Alternative 1
10
13
9
Decision Alternative 2
15
9
10
[4] What should the probabilities of states of nature 2
and 3 be so that the expected values of the two decision
alternatives...

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