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Events alternative A1 A2 A3 Probabilities following table: SI 27 45 52 Ihe monetary payoffs of cach combination of A, and S are given in the ol any one of he four possible evets Si 12 17 36 0.,3 Answer following based on the information is given above 0.4 c) By using minmax regrct identify lowest regrets (3pts) S3 14 ) compute amount of expected monetary value (3pis) 35 g) What is value of expected opportunity losses (3pts?) 29 h) what is expected value of perfect infomation(3pts) 0.2 $4 26 A) Tdentify the best alternatives that maximize profit and minimize the costs by usine ma approaches (2pts) 20 b) ldentify the best alternatives that ımaximize profit and minimize the costs by using m approaches (2pts) 15 0.10 d) ldentify the best alternatives that maximize profit and ninimize the costs by usir approaches(2pts) e) ldentity the best alternatives that maximize profit and minimize the costs by criteria at u-0.60(3pts)

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To answer your questions about the decision-making problem using the provided probabilities and payoffs, let’s first format the data you have given.

It seems like you have a decision matrix with alternatives (A1, A2, A3) and states of nature (S1, S2, S3) along with their probabilities and corresponding payoffs.

Here's a rough summary based on your input:

Payoff Table:

| Alternatives | S1 | S2 | S3 | Probability | |--------------|------|------|------|-------------| | A1 | 12 | 17 | 36 | 0.3 | | A2 | 27 | 45 | 52 | 0.4 | | A3 | 14 | 20 | 35 | 0.2 |

Step 1: Calculating Expected Monetary Value (EMV)

To calculate EMV for each alternative, use the formula: \[ \text{EMV} = \sum (\text{Payoff} \times \text{Probability}) \]

EMV for A1:

\[ \text{EMV}_{A1} = (12 \times 0.3) + (17 \times 0.4) + (36 \times 0.2) = 3.6 + 6.8 + 7.2 = 17.6 \]

EMV for A2:

\[ \text{EMV}_{A2} = (27 \times 0.3) + (45 \times 0.4) + (52 \times 0.2) = 8.1 + 18 + 10.4 = 36.5 \]

EMV for A3:

\[ \text{EMV}_{A3} = (14 \times 0.3) + (20 \times 0.4) + (35 \times 0.2) = 4.2 + 8 + 7 = 19.2 \]

Conclusion on EMV

  • EMV of A1 = 17.6
  • EMV of A2 = 36.5 (Best choice)
  • EMV of A3 = 19.2

Step 2: Minimax Regret Approach

To apply the minimax regret approach, the first step is to find the maximum payoff for each state of nature:

  • Maximum for S1 = 27 (A2)
  • Maximum for S2 = 45 (A2)
  • Maximum for S3 = 52 (A2)

Now we can create the regret table by calculating the regret for each alternative:

| Alternatives | S1 Regret | S2 Regret | S3 Regret | Maximum Regret | |--------------|-----------|-----------|-----------|-----------------| | A1 | 15 (27-12)| 28 (45-17)| 16 (52-36)| 28 | | A2 | 0 | 0 | 0 | 0 | | A3 | 13 (27-14)| 25 (45-20)| 17 (52-35)| 25 |

From the table, the maximum regret for each alternative is:

  • A1: 28
  • A2: 0 (Best)
  • A3: 25

Conclusions for Regret

The best alternative using the minimax regret is A2 since it has the lowest maximum regret (0).

Step 3: Expected Opportunity Loss (EOL)

EOL is the weighted sum of regrets:

\[ EOL = \sum (\text{Regret} \times \text{Probability}) \]

For A1: \[ EOL_{A1} = (15 \times 0.3) + (28 \times 0.4) + (16 \times 0.2) = 4.5 + 11.2 + 3.2 = 18.9 \]

For A2 (no regrets): \[ EOL_{A2} = 0 \]

For A3: \[ EOL_{A3} = (13 \times 0.3) + (25 \times 0.4) + (17 \times 0.2) = 3.9 + 10 + 3.4 = 17.3 \]

Conclusions for EOL

  • EOL of A1 = 18.9
  • EOL of A2 = 0
  • EOL of A3 = 17.3

Expected Value of Perfect Information (EVPI)

EVPI is calculated as: \[ EVPI = \text{Maximum EMV with perfect information} - \text{Highest EMV without perfect information} \]

The maximum EMV is for A2, which is 36.5. So now we calculate: \[ EVPI = 36.5 - 36.5 = 0 \]

Final Recommendations

A2 is the best alternative to choose since it maximizes the profit and minimizes the costs by both EMV and minimax regret criteria. The calculations for opportunity losses and EVPI suggest the same outcome.

If you need assistance on other specific approaches, feel free to ask!