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MIT15_053S13_rec10sol

# MIT15_053S13_rec10sol - Optimization Methods in Management...

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Optimization Methods in Management Science MIT 15.053, Spring 2013 Recitation 10, Friday May 3th, 2013 Problem 1 The Airfare Problem 1 . You are trying to get the cheapest airfare that you can. You just called up and found that the ticket home will cost \$400, and it cannot be refunded or exchanged. You can also buy a ticket for \$450, which can be refunded for \$430 (and thus costs you \$20). The price of tickets will change in one week, and you will have one more chance to buy a ticket. There is a 50% chance that the ticket would cost \$300, and a 50% chance that it would cost \$600. What should you do to minimize the expected expense? Write the Airfare problem as a decision tree, and solve it. Solution. The decision tree is: The optimal decision is to buy the refundable ticket for \$450, and then wait to see what the price of the airline ticket is the second time. If the price is \$300, refund the old ticket (for \$430) and buy the ticket at \$300, paying a total of \$320. If the price is \$600, keep the refundable ticket you bought. The expected cost of your ticket is \$385. Problem 2 1 This problem is also discussed in the class.

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Value of Information Suppose Tom is at a carnival and while there he sees a green monkey stuffed animal that he would like to have. In order to win the stuffed monkey Tom needs to play a game that costs \$1. In the game there are 5 shells and a ball that is hidden behind
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