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Payoffs, Matrices, and Decision Trees

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Sapphire Weekday is a restaurant chain and it allows three franchising option for investors. The full franchising option charges an investor $100,000 every year but allow the investor to keep all the profit. The half franchising option charges an investor $30,000 and allows the investor to keep 50% of the profit. The fixed franchising option pays an investor $25,000 every year with no profit sharing.

Joan Joyce is considering opening up a Sapphire Weekday franchise in Haleiwa. She estimated that if the business is good, the profit of the restaurant would be about $200,000, but if the business is bad, the profit would only be about $100,000. Forecast indicates that 30% of the time the business will be good and 70% it will be bad. Which would be her best option based on the following criterion?

a) Maximax (aggressive)
b) Maximin (conservative)
c) Minimax regret (opportunity loss)
d) In addition, construct a decision tree and compute the rollback values to find the best expected value decision.

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