Title: Decision-Making Using the Hurwicz Criterion**Payoff Matrix and Decision Analysis**Consider the payoff matrix below featuring actions, states of nature, and prior probabilities:| | 0.20 (s₁) | 0.30 (s₂) | 0.50 (s₃) ||---------------|-----------|-----------|-----------|| **a₁** | 3 | 5 | 2 || **a₂** | 1 | 6 | 4 || **a₃** | 4 | 4 | -1 |**Decision Problem:***Goal:* Identify the optimal action using the Hurwicz criterion with an optimism index (α) of 0.6. The Hurwicz criterion is a decision rule in which a linear combination of the best and worst payoff for each action is calculated, using the given index of optimism. Ignore prior probabilities when making your decision.**Steps to Apply the Hurwicz Criterion:**1. **Calculate for Each Action:** - Maximum Payoffs: - a₁: max(3, 5, 2) = 5 - a₂: max(1, 6, 4) = 6 - a₃: max(4, 4, -1) = 4 - Minimum Payoffs: - a₁: min(3, 5, 2) = 2 - a₂: min(1, 6, 4) = 1 - a₃: min(4, 4, -1) = -12. **Calculate Hurwicz Criterion Value for Each Action:** - a₁: [0.6 * 5] + [0.4 * 2] = 3 + 0.8 = 3.8 - a₂: [0.6 * 6] + [0.4 * 1] = 3.6 + 0.4 = 4.0 - a₃: [0.6 * 4] + [0.4 * (-1)] = 2.4 - 0.4 = 2.0**Decision:**Choose the action with the highest value according to

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Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

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Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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