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Unformatted text preview: 3). Prove that Simplex will never cycle if an LP has the property that for every degenerate BFS the winner of the min ratio test is unique. 4). Consider the following LP: min z = 2 x 1 + 15 x 2 + 5 x 3 + 6 x 4 s . t . x 1 + 6 x 2 + 3 x 3 + x 4 22 x 1 + 5 x 2x 3 + 3 x 4 3 x 1 , x 2 , x 3 , x 4 (a). Give the dual of the LP. (b). Solve the dual geometrically. (c). From the solution of the dual problem, nd the solution of the original problem. Reminder: The midterm is Thursday October 21 in class, covering material from homeworks 15. The exam is closed notes. However, you may bring 1 page of notes, written by you (not typed or xeroxed). This page will be turned in with the exam....
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 Fall '08
 Arkin,E

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