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(a) Change the right-hand sides to b₁ [20] 30

(a) Change the right-hand sides to b₁ [20] 30

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 3BEXP
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(a) Abj = -10, Ab2 = 20 -10 + AZ* = (0 2) = 40 20 Al; = (1 -1)) -30 20 –10 Ab, = (0 1) = 20 20 Revised Final Tableau: Bas | Eq| Var | No| Z| Coefficient of | Right X1 x2 X3 X4 X5 side Z| 01 1| X4| 1| 01 X1| 2| 01 1 1 60 -1 5 1 -1 -10 1 4 -1 30 The current basic solution is superoptimal, but infeasible. Revised Final Tableau After Reoptimization (Dual Simplex Method) : Bas | Eq| Var | No| Z| | Right X5 Coefficient of X1 x2 X3 X4 side Z| 01 1|0.333 X2| 1| 010.333 X5| 2| 01-0.33 O 12.33 2.333 1 1.333 0.333 O -6.33 -1.33 | 46.67 | 6.667 | 3.333 1.
Transcribed Image Text:(a) Abj = -10, Ab2 = 20 -10 + AZ* = (0 2) = 40 20 Al; = (1 -1)) -30 20 –10 Ab, = (0 1) = 20 20 Revised Final Tableau: Bas | Eq| Var | No| Z| Coefficient of | Right X1 x2 X3 X4 X5 side Z| 01 1| X4| 1| 01 X1| 2| 01 1 1 60 -1 5 1 -1 -10 1 4 -1 30 The current basic solution is superoptimal, but infeasible. Revised Final Tableau After Reoptimization (Dual Simplex Method) : Bas | Eq| Var | No| Z| | Right X5 Coefficient of X1 x2 X3 X4 side Z| 01 1|0.333 X2| 1| 010.333 X5| 2| 01-0.33 O 12.33 2.333 1 1.333 0.333 O -6.33 -1.33 | 46.67 | 6.667 | 3.333 1.
DI 6.7-4. Consider the following problem. Мaximize Z = 2x1 + 7x2 – 3x3, subject to x1 + 3x2 + 4xz < 30 X1 + 4x2 X3 < 10 - and x¡ 2 0, x2 2 0, Xz 2 (0. By letting x4 and x5 be the slack variables for the respective con- straints, the simplex method yields the following final set of equations: + 2x5 = 20 X5 = 20 + x5 = 10. z + x2 + X3 (0) (1) (2) x2 + 5x3 + x4 – X1 + 4x2 - X3 Now you are to conduct sensitivity analysis by independently in- vestigating each of the following seven changes in the original model. For each change, use the sensitivity analysis procedure to revise this set of equations (in tableau form) and convert it to proper form from Gaussian elimination for identifying and eval- uating the current basic solution. Then test this solution for fea- sibility and for optimality. If either test fails, reoptimize to find a new optimal solution. (a) Change the right-hand sides to Г20 b2 (30 (b) Change the coefficients of x3 to C3 -27 a13 a23. 3. ||
Transcribed Image Text:DI 6.7-4. Consider the following problem. Мaximize Z = 2x1 + 7x2 – 3x3, subject to x1 + 3x2 + 4xz < 30 X1 + 4x2 X3 < 10 - and x¡ 2 0, x2 2 0, Xz 2 (0. By letting x4 and x5 be the slack variables for the respective con- straints, the simplex method yields the following final set of equations: + 2x5 = 20 X5 = 20 + x5 = 10. z + x2 + X3 (0) (1) (2) x2 + 5x3 + x4 – X1 + 4x2 - X3 Now you are to conduct sensitivity analysis by independently in- vestigating each of the following seven changes in the original model. For each change, use the sensitivity analysis procedure to revise this set of equations (in tableau form) and convert it to proper form from Gaussian elimination for identifying and eval- uating the current basic solution. Then test this solution for fea- sibility and for optimality. If either test fails, reoptimize to find a new optimal solution. (a) Change the right-hand sides to Г20 b2 (30 (b) Change the coefficients of x3 to C3 -27 a13 a23. 3. ||
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