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Consider the following Integer Linear Program: Minimise: 5x1 4x2 Subject to: X1 + X2 > 6 X1 + 4x2 > 12 3x1 + X2 > 9 X₁, X2 ≥ 0 and integer Construct the initial tableau for this problem including all decision, slack and artificial variables. You should assume the M-method will be used to solve this, so build the tableau with the objective function (i) +

Consider the following Integer Linear Program: Minimise: 5x1 4x2 Subject to: X1 + X2 > 6 X1 + 4x2 > 12 3x1 + X2 > 9 X₁, X2 ≥ 0 and integer Construct the initial tableau for this problem including all decision, slack and artificial variables. You should assume the M-method will be used to solve this, so build the tableau with the objective function (i) +

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter3: Introduction To Optimization Modeling
Section: Chapter Questions
Problem 41P
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Consider the following Integer Linear Program: Minimise: 5x₁ + 4x2 Subject to: X1 X1 3x1 (1) + (iii) X2 4x2 > 6 12 + + X2 ≥ 9 X₁, X2 ≥ 0 and integer Construct the initial tableau for this problem including all decision, slack and artificial variables. You should assume the M-method will be used to solve this, so build the tableau with the objective function coefficients for any artificial variables set to -M. (ii) In the optimal solution to the (non-integer) relaxation of this problem, X₁ and X2 are both basic and the second constraint is a strict inequality. Using any method you like (including computer software), derive the transformation matrix for the optimal solution to the relaxation of this problem, and use it to construct an optimal tableau for the non-integer LP (you can assume that the solution is feasible, so no columns for the artificial variables are needed). From the tableau you derived in (ii) above, use the dual simplex method to find the optimal solution to the integer LP. You should examine (at least) two distinct additional constraints on one of the decision variables to verify that your solution is optimal for the integer LP
Transcribed Image Text:Consider the following Integer Linear Program: Minimise: 5x₁ + 4x2 Subject to: X1 X1 3x1 (1) + (iii) X2 4x2 > 6 12 + + X2 ≥ 9 X₁, X2 ≥ 0 and integer Construct the initial tableau for this problem including all decision, slack and artificial variables. You should assume the M-method will be used to solve this, so build the tableau with the objective function coefficients for any artificial variables set to -M. (ii) In the optimal solution to the (non-integer) relaxation of this problem, X₁ and X2 are both basic and the second constraint is a strict inequality. Using any method you like (including computer software), derive the transformation matrix for the optimal solution to the relaxation of this problem, and use it to construct an optimal tableau for the non-integer LP (you can assume that the solution is feasible, so no columns for the artificial variables are needed). From the tableau you derived in (ii) above, use the dual simplex method to find the optimal solution to the integer LP. You should examine (at least) two distinct additional constraints on one of the decision variables to verify that your solution is optimal for the integer LP
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