final-exam - MthSc 810 Mathematical Programming Final exam....

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Unformatted text preview: MthSc 810 Mathematical Programming Final exam. Due Tuesday, December 13, 6pm EST. Full name braceleftbigg Signature braceleftbigg You have seven days and seven problems. This exam accounts for 25% of the final grade. There are 105 points. Please write clear and concise statements. Explain all your answers. Use a readable handwriting: un- readable answers will be given no points. Turn in your final exam stapled with this first page bearing your name and signature. This is an exam, therefore you must work on your own . For more information, check http://www.clemson.edu/academics/academic-integrity . Problem 1 (5 pts.): 1. Prove that the set S = { ( x 1 ,x 2 ) : x 1 x 2 1 ,x 1 > ,x 2 > } is convex. 2. Prove that the set G = { R + : 1 min { x : x 1 }} is convex. Problem 2 (15 pts.): Consider the problem min- 3 x 1 + x 2 s.t. x 1- x 2- x 3 = 1 2 x 1- x 2 + x 4 = 4 x 1 , x 2 , x 3 , x 4 . 1. The basis B = { 2 , 4 } is neither primal nor dual feasible. However, there is one pivoting operation that suffices to obtain a basis that is either primal...
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This note was uploaded on 03/14/2012 for the course MTHSC 810 taught by Professor Staff during the Fall '08 term at Clemson.

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final-exam - MthSc 810 Mathematical Programming Final exam....

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