hw3 - (c). The current BFS is degenerate. (d). The current...

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AMS 540 / MBA 540 (Fall, 2010) Estie Arkin Homework Set # 3 Due in class on Thursday, September 30, 2010. 1). (a). State a non degenerate BFS for the following LP: (make sure to say which variables are basic, which are non basic and what each variable is equal to.) max z = 6 x 1 + 4 x 2 + x 3 s . t . 2 x 1 + x 2 + x 3 2 x 1 1 x 1 , x 2 , x 3 0 (b). State a degenerate BFS for the LP in part (a). 2). Consider the following tableau for a minimization LP: State conditions on a 1 , a 2 , a 3 , b , c 1 , c 2 that are required to make the following statements true (each part is independent of the others). z x 1 x 2 x 3 x 4 x 5 x 6 RHS z 1 c 1 c 2 0 0 0 0 10 x 3 0 4 a 1 1 0 a 2 0 b x 4 0 -1 -5 0 1 -1 0 2 x 6 0 a 3 -3 0 0 -4 1 3 (a). The current BFS is optimal. (b). The current basic solution is not feasible.
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Unformatted text preview: (c). The current BFS is degenerate. (d). The current basic solution is feasible but the LP is unbounded. (e). The current basic solution is feasible but the objective function can be improved by replacing x 6 as a basic variable with x 1 . 3). Suppose we have a BFS that is nondegenerate. Further suppose that an improving nonbasic variable x k enters the basis. Prove that if the minimum ratio test for choosing a leaving variable has a unique variable achieving the minimum, x B r , then the next BFS is also non-degenerate....
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This note was uploaded on 01/31/2011 for the course AMS 540 taught by Professor Arkin,e during the Fall '08 term at SUNY Stony Brook.

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