IEOR E4004: Introduction to Operations Research: Determ

IEOR E4004: Introduction to Operations Research: Deterministic Models Jay Sethuraman & Dawn Strickland HW 8 (due 12/07) Problems not written out explicitly are from the text: Applied Mathematical Program- ming by Bradley Hax and Magnanti. 1. Problem 9.2 2. Problem 9.8 3. Problem 9.9 4. Problem 9.15 5. Formulate an integer program that will determine if it is possible to place 4 queens on a 4-by-4 chessboard so that no queen can capture another queen. (A queen can move as many spaces as she wants in the vertical horizontal or diagonal direction.) 6. Suppose you are visiting a forest in which every inhabitant is either a knight or a knave. Knights always tell the truth and knaves always lie. In addition some of the inhabitants are werewolves who can be either a knight or a knave. You are interviewing two of the three inhabitants A B and C. It is known that exactly one of them is a werewolf. They make the following statements: A. At least one of the three of us is a knave. B. C is a knight. Given that there is exactly one werewolf and that he is a knight formulate an integer program that will determine which inhabitant is the werewolf. 1
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