Construct the decision tree.

Question

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Answer 1

Question

Chapter 12, Problem 1P

a.

To determine

Construct the decision tree.

a.

Expert Solution

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

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.

Decision	Maximum Profit	Minimum Profit
d₁	250	25
d₂	100	75

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	s₁	s₂	s₃
d₁	0	0	50
d₂	150	0	0

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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Students have asked these similar questions

The following payoff table provides profits based on various possible decision alternatives and various levels of demand. ALTERNATIVE DEMAND LOW MEDIUM HIGH Alternative 1 40 80 150 Alternative 2 80 120 130 Alternative 3 100 100 100 a. Which alternative would a pessimist choose? b. Which alternative would an optimist choose? c. Which alternative should be chosen using the Hurwicz decision criterion with α = 0.4?

The following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature.

n the book Business Research Methods (5th ed.), Donald R. Cooper and C. William Emory discuss a market researcher for an automaker who is studying consumer preferences for styling features of larger sedans. Buyers, who were classified as “first-time” buyers or “repeat” buyers, were asked to express their preference for one of two types of styling—European styling or Japanese styling. Of 40 first-time buyers, 11 preferred European styling and 29 preferred Japanese styling. Of 60 repeat buyers, 41 preferred European styling and 19 preferred Japanese styling. (a) Set up a contingency table for these data. (b) Test the hypothesis that buyer status (repeat versus first-time) and styling preference are independent at the .05 level of significance. What do you conclude? (Round your answer to 3 decimal places.)

Answer 2

Question

Chapter 12, Problem 1P

a.

To determine

Construct the decision tree.

a.

Expert Solution

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

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.

Decision	Maximum Profit	Minimum Profit
d₁	250	25
d₂	100	75

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	s₁	s₂	s₃
d₁	0	0	50
d₂	150	0	0

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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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Question

Chapter 12, Problem 1P

a.

To determine

Construct the decision tree.

a.

Expert Solution

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

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.

Decision	Maximum Profit	Minimum Profit
d₁	250	25
d₂	100	75

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	s₁	s₂	s₃
d₁	0	0	50
d₂	150	0	0

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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Answer 4

Question

Chapter 12, Problem 1P

a.

To determine

Construct the decision tree.

a.

Expert Solution

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

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.

Decision	Maximum Profit	Minimum Profit
d₁	250	25
d₂	100	75

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	s₁	s₂	s₃
d₁	0	0	50
d₂	150	0	0

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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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 12, Problem 1P

a.

To determine

Construct the decision tree.

a.

Expert Solution

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

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.

Decision	Maximum Profit	Minimum Profit
d₁	250	25
d₂	100	75

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	s₁	s₂	s₃
d₁	0	0	50
d₂	150	0	0

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.

Answer 6

Chapter 12, Problem 1P

a.

To determine

Construct the decision tree.

a.

Expert Solution

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.

Answer 7

Chapter 12, Problem 1P

a.

To determine

Construct the decision tree.

Answer 8

a.

Expert Solution

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.

Answer 9

a.

Expert Solution

Answer 10

a.

Expert Solution

Answer 11

Expert Solution

Answer 12

b.

To determine

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

b.

Expert Solution

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.

Decision	Maximum Profit	Minimum Profit
d₁	250	25
d₂	100	75

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	s₁	s₂	s₃
d₁	0	0	50
d₂	150	0	0

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.

Answer 13

b.

To determine

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

Answer 14

b.

Expert Solution

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.

Answer 15

b.

Expert Solution

Answer 16

b.

Expert Solution

Answer 17

Expert Solution

Answer 18

Explanation of Solution

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

Decision	Maximum Profit	Minimum Profit
d₁	250	25
d₂	100	75

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: