### Decision Analysis Based on Profit MatrixWhen making decisions based on different scenarios, it is important to consider various decision-making criteria. Below is the given profit matrix, which will be used to decide the best alternative by considering Expected Value, Savage Regret Minimax, and EVPI (Expected Value of Perfect Information).#### Profit Matrix:| Probability | S1 (0.20) | S2 (0.30) | S3 (0.50) ||-------------|-----------|-----------|-----------|| A | 50 | -10 | 90 || B | 80 | 0 | 50 || C | 40 | 20 | 60 |#### Decision Criteria:1. **Expected Value**: - Calculate the expected profit for each alternative. - Formula: \[ EV = (Probability\ of\ S1 \times Profit\ in\ S1) + (Probability\ of\ S2 \times Profit\ in\ S2) + (Probability\ of\ S3 \times Profit\ in\ S3) \]2. **Savage Regret Minimax**: - Calculate the regret for each alternative in each state. - Regret is the difference between the highest possible profit in a state and the profit obtained by that alternative in the same state. - Use these regrets to determine the minimax decision, which minimizes the maximum regret. 3. **EVPI (Expected Value of Perfect Information)**: - Calculate EVPI which represents the average amount we would be willing to pay to gain perfect information. - Formula: \[ EVPI = (Maximum\ of \ Expected\ Value\ for\ each\ state) - (Expected\ Value\ of\ the\ optimal\ alternative\ without\ perfect\ information) \]### Steps to Draw Decision Tree and Decide Based on Each Criterion:1. **Expected Value**: - Calculate for each alternative. - Example calculation for Alternative A: \[ EV_A = 0.20(50) + 0.30(-10) + 0.50(90) = 10 + (-3) + 45 = 52 \] 2. **Savage Regret Minimax**: - Identify the maximum profit for each state. - Calculate regret for each alternative.

Answered: Given the following profit matrix. Draw…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter9: Decision Making Under Uncertainty

Section9.2: Elements Of Decision Analysis

Problem 2P

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Given the following profit matrix. Draw the decision tree and decide which alternative you choose based on: probability (-20) (.30) (50) a. Expected Value $1 $2 $3 b. Savage regret minimax A 50 -10 c. EVPI B 80 0 C 20 Alternate 40 90 50 60