Essentials Of Business Analytics
Essentials Of Business Analytics
1st Edition
ISBN: 9781285187273
Author: Camm, Jeff.
Publisher: Cengage Learning,
Question
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Chapter 12, Problem 1P

a.

To determine

Construct the decision tree.

a.

Expert Solution
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Explanation of Solution

Here, there are two decision alternatives d1 and d2 and the three states of nature s1, s2  and s3.

Thus, the decision tree is given as follows:

Essentials Of Business Analytics, Chapter 12, Problem 1P

Thus, the decision tree has been constructed.

b.

To determine

Find the decision using the optimistic, conservative and minimax regret approaches.

b.

Expert Solution
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Answer to Problem 1P

The decision d1 gives the optimistic approach because it has the largest maximum profit.

The decision d2 gives the conservative approach because it has the largest minimum profit.

The minimax regret is the decision d1 because it minimizes the maximum regret.

Explanation of Solution

By using the decision tree in Part (a), the maximum and minimum profit based on the decisions d1 and d2.

DecisionMaximum ProfitMinimum Profit
d125025
d210075

Optimistic approach:

The optimistic approach evaluates each decision alternative in terms of best payoff that can occur.

The decision d1 gives the optimistic approach because it has the largest maximum profit (from the above table).

Conservative approach:

The conservative approach evaluates each decision alternative in terms of worst payoff that can occur.

The decision d2 gives the conservative approach because it has the largest minimum profit (from the above table).

Minimax Regret approach:

The minimax regret approach is the difference between the payoff associated with a particular alternative and payoff associated with the most decision that would yield the most desirable payoff for a given state of nature.

Regret or opportunity loss table:

Decision

s1s2s3
d10050
d215000

The maximum regret for the decision d1 is 50 and d2  is 150.

Here, the decision d1 has been selected because it minimizes the maximum regret.

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