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sol3 - AMS 540 MBA 540(Fall 2010 Estie Arkin Homework Set 3...

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AMS 540 / MBA 540 (Fall, 2010) Estie Arkin Homework Set # 3: Solution notes 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 is variable is equal to.) max z = 6 x 1 + 4 x 2 + x 3 s . t . x 1 + x 2 + x 3 1 x 1 1 x 1 , x 2 , x 3 0 Introduce slack variables s 1 ,s 2 in the first and second constraints to get standard form (remem- ber that Basic Solutions are defined only for standard form). max z = 6 x 1 + 4 x 2 + x 3 s . t . x 1 + x 2 + x 3 + s 1 = 1 x 1 + s 2 = 1 x 1 , x 2 , x 3 , s 1 , s 2 0 Let a BFS be s 1 = s 2 = 1 basic variables (non degenerate) and x 1 = x 2 = x 3 = 0 non basic. (Recall, the number of basic variables must be m , the number of constraints, which is 2 in our case.) (b). State a degenerate BFS for the LP in part (a). Basic variables x 1 = 1 and x 2 = 0 (degenerate), x 3 = s 1 = s 2 = 0 non basic. 2). (a). The current BFS is optimal. c 1 0, c 2 0, (optimality) b 0 (feasible). (b). The current basic solution is not feasible. b < 0.
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