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Additional Problems (Classes #2 and #3) Page 1 Given the following payoff table: Decision State 1 State 2 State 3 State 4 #1 4 –9 0 0 #2 7 9 4 3 #3 –2 3 –1 –1 #4 6 6 –6 –2 #5 –9 0 7 9 #6 –7 –3 8 –6 What would be the decision ( not the value! ) based on: Maximax criteria? #2, #5 Maximin criteria? #2 Minimax regret? #2 EMV when the states have equal probabilities of occurring? #2 Note: There may be multiple answers. All answers must be listed credit. Worksheets (not graded!) Decision Maximum Minimum EMV #1 #2 #3 #4 #5 #6 Regret (Opportunity Loss) Table Decision State 1 State 2 State 3 State 4 Maximum #1 #2 #3 #4 #5 #6

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Additional Problems (Classes #2 and #3) Page 2 Using the decision tree in the right column, calculate the value (round to a maximum of 2 decimal places) at nodes 1 through 14. The probabilities in the decision tree are below their associated branches. Assume that the payoffs are profits. Node Value Node Value 1 6.12 2 5.93 Node Value Node Value 3 5.7 9 7.0 4 2.7 10 8.1 5 4.6 11 2.2 6 5.2 12 5.0 7 6.4 13 4.2 8 3.5 14 4.8 Determine the decision at nodes A through E. Indicate the decision by placing an “ X ” in the appropriate branch for each node. Node Top Middle Bottom A X XXXXXXX B X C X D X E X 1 7 3 2 8 4 4 3 2 3 5 9 1 B 1 6 9 7 9 7 1 3 7 8 2 2 C 2 8 9 8 6 9 10 9 6 0 11 4 1 D 3 12 4 6 4 13 3 7 9 14 3 5 E A (0.5) (0.3) (0.2) (0.1) (0.5) (0.4) (0.2) (0.4) (0.4) (0.4) (0.3) (0.3) (0.6) (0.1) (0.3) (0.3) (0.4) (0.3) (0.3) (0.2) (0.5) (0.3) (0.4) (0.3) (0.3) (0.5) (0.2) (0.2) (0.2) (0.6) (0.4) (0.4) (0.2) (0.2) (0.5) (0.3) (0.3) (0.7) (0.4) (0.6)
Additional Problems (Classes #2 and #3) Page 3 Dr. Mark is planning on purchasing raffle tickets for a charity for \$1.00 each. The only prize is a gift certificate worth \$1,000. He knows that a total of 1,900 tickets have been sold to other people. He has the option of purchasing either 10, 20, or 30 tickets (he must buy the tickets in quantities of 10) Complete the payoff table. The payoff values in the table are the net winnings (value of the raffle minus the cost of the tickets).

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• Fall '12
• MarkAnthonyChristobek
• Additional Problems, Dr. Mark, Mrs. Hanover

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