Consider the following linear program: maximize subject to 3x1 + 4x2 + 3x3 + 6x4 2x1...

Transcribed Image Text:

Consider the following linear program: maximize subject to 3x1 + 4x2 + 3x3 + 6x4 2x1 + x2-x3 + x4 x1 + x2 + x3 + x4 -x2 + 2x3 + x4 X1, X2, x3, x4 > 12 = 8 ≤ 10 ≥ 0. (1) After transforming the problem into standard form and apply Simplex method, we obtain the final tableau as follow: B 0 2 9 0 3 0 36 1 1 0 -2 0 -1 0 4 4 0 1 3 1 1 0 4 6 0 -2 -1 0 -1 1 6 a) Derive the dual problem of the linear program (1) and calculate a dual solution based on complementarity conditions. Given that the optimal solution to the primal solution is unique, investigate whether the dual solution is unique. b) Do the optimal primal solution and the objective function value change if we • decrease the objective function coefficient for x3 to 1? • increase the objective function coefficient for x3 to 12? . decrease the objective function coefficient for x₁ to 1? • increase the objective function coefficient for x₁ to 7? e) Find the possible range for adjusting the coefficient 8 of the second constraint such that the current basis is kept optimal. Consider the following linear program: maximize subject to 3x1 + 4x2 + 3x3 + 6x4 2x1 + x2-x3 + x4 x1 + x2 + x3 + x4 -x2 + 2x3 + x4 X1, X2, x3, x4 > 12 = 8 ≤ 10 ≥ 0. (1) After transforming the problem into standard form and apply Simplex method, we obtain the final tableau as follow: B 0 2 9 0 3 0 36 1 1 0 -2 0 -1 0 4 4 0 1 3 1 1 0 4 6 0 -2 -1 0 -1 1 6 a) Derive the dual problem of the linear program (1) and calculate a dual solution based on complementarity conditions. Given that the optimal solution to the primal solution is unique, investigate whether the dual solution is unique. b) Do the optimal primal solution and the objective function value change if we • decrease the objective function coefficient for x3 to 1? • increase the objective function coefficient for x3 to 12? . decrease the objective function coefficient for x₁ to 1? • increase the objective function coefficient for x₁ to 7? e) Find the possible range for adjusting the coefficient 8 of the second constraint such that the current basis is kept optimal.

Answer rating: 100% (QA)

Problem a 1 Derive the dual problem of the linear program 1 The dual problem of a linear program is a problem that is formulated by interchanging the ... View the full answer