Final answer:
To determine the decision alternative that will maximize the expected payoff under different demand probabilities, calculate the expected payoff for each alternative by multiplying each payoff in the table by its corresponding probability. The alternative with the highest expected payoff is the one that will maximize the expected payoff.
Step-by-step explanation:
The decision alternative that will maximize the expected payoff under different demand probabilities can be determined by calculating the expected payoff for each alternative. To do this, we multiply each payoff in the table by its corresponding probability and sum up the results. The alternative with the highest expected payoff is the one that will maximize the expected payoff.
For example, if the payoff table is as follows:
Decision AlternativeLow DemandMedium DemandHigh DemandAlternative A$10$20$30Alternative B$15$25$35Alternative C$5$10$25
The expected payoffs for each alternative are:
Expected payoff for Alternative A = (0.2 * $10) + (0.4 * $20) + (0.4 * $30) = $10 + $8 + $12 = $30
Expected payoff for Alternative B = (0.2 * $15) + (0.4 * $25) + (0.4 * $35) = $3 + $10 + $14 = $27
Expected payoff for Alternative C = (0.2 * $5) + (0.4 * $10) + (0.4 * $25) = $1 + $4 + $10 = $15
Therefore, Alternative A has the highest expected payoff of $30 and will maximize the expected payoff under different demand probabilities.