Question

**Q5.** The following is a payoff table giving
profits for various situations.

State of Nature |
|||

Alternatives |
A |
B |
C |

Alternative 1 |
120 |
140 |
120 |

Alternative 2 |
200 |
100 |
50 |

Alternative 3 |
100 |
120 |
180 |

Do Nothing |
0 |
0 |
0 |

What decision should be made based on the minimax regret criterion?

- Alternative 1
- Alternative 2
- Alternative 3
- Do Nothing

Answer #1

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...

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...

A manager has developed a payoff table that indicates the
profits associated with a set of alternatives under two possible
states of nature.
Alt S1 S2
1 10 2
2 -2 8
3 8 5
If the manager uses maximin as the decision criterion, which of
the alternatives should she choose?
A.
Alternative 1
B.
Alternative 2
C.
Alternative 3
D.
None of the above

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 _____.

5. [5 marks] Suppose you have the following payoff
table.
Alternatives
States of Nature
A (0.5)
B (0.5)
1
$650,000
$450,000
2
$200,000
$475,000
3
$300,000
$250,000
Draw a decision tree. Include the expected monetary values and
prior probabilities for each state of nature. Show all of your
work. Make sure each branch is appropriately labelled. Based on
your expected monetary values, which alternative do you choose
(answer in a single sentence)?

5. [5 marks] Suppose you have the following payoff
table.
Alternatives
States of Nature
A (0.5)
B (0.5)
1
$650,000
$450,000
2
$200,000
$475,000
3
$300,000
$250,000
Draw a decision tree. Include the expected monetary values and
prior probabilities for each state of nature. Show all of your
work. Make sure each branch is appropriately labelled. Based on
your expected monetary values, which alternative do you choose
(answer in a single sentence)?

State
of
Nature
Decision Alternative
s1
s2
s3
s4
d1
600
400
-100
120
d2
700
-200
0
400
d3
700
-200
0
400
P(si)
0.3
0.4
0.2
0.1
For a lottery having a payoff 700 with probability p and -200
with probability (1-p), the decision maker expressed the following
indifference probability. Suppose U (700) =100 and U (-200)
=-10.
Payoff
Indifferent Probability
600
0.95
400
0.8
120
0.5
0
0.35
-100
0.2
a) Complete the utility table by using...

Consider the following payoff table that represents the
profits earned for each alternative (A, B, and C) under the states
of nature S1, S2, and S3.
S1 S2 S3
A $60 $145 $120
B $75 $125 $110
C $95 $85 $130
Refer to the payoff table. What is the expected value of
perfect information (EVPI)? Assume P(S1) = 0.5 and P(S2) = 0.25.
(Points : 2)

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...

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