# sol6 - AMS 540 MBA 540(Fall 2010 Estie Arkin Homework Set 6...

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AMS 540 / MBA 540 (Fall, 2010) Estie Arkin Homework Set # 6: Solution notes 1). Since { max cx | Ax = b, x 0 } has a fnite optimal solution, its dual also has a fnite optimal solution, which obviously implies it is ±easible. Changing the primal constratint’s right hand side changes the dual objective ±unction only, there±or the dual o± the problem { max cx | Ax = b , x 0 } has a ±easible solution. This implies that the problem { max cx | Ax = b , x 0 } is either in±easible or has a fnite optimal solution, but cannot be unbounded! Note that we cannot conclude that the original problem has a bounded ±easible region just because the LP is bounded, this may not be true! 2). We multiply the constraints by -1, then add slack variables s 1 and s 2 to get the frst tableau ±or dual simplex: z x 1 x 2 x 3 s 1 s 2 rhs 1 2 0 1 0 0 0 0 -1 -1 1 1 0 -5 0 -1 2 -4 0 1 -8 This tableau is “optimal” ±or the max problem, but not ±easible, so we pivot out s 2 and do the min ratio test, min { z j - c j / - y

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sol6 - AMS 540 MBA 540(Fall 2010 Estie Arkin Homework Set 6...

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