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Consider the following optimization problem: MIN: X₁ + X₂ Subject to: -4X₁ + 4X₂ ≤ 1 -8X₁ + 12x₂ 2 13 X1 X2 20 (a) What is the optimal solution to this LP problem? (b) Now suppose that X₁ and X₂ must be integers. What is the optimal solution? (X₁, X₂) - (c) What general principle of integer programming is illustrated by this question? O The optimal integer solution to an ILP is not, in general, also a basic feasible solution to the continuous LP. The optimal objective function value of a minimization ILP is always higher than that of the continuous solution. The optimal integer solution to an ILP cannot, in general, be obtained by rounding the continuous solution. The optimal integer solution to an ILP is, in general, also an optimal solution to the continuous LP. O The optimal objective function value of a minimization ILP is always smaller than that of the continuous solution.

Consider the following optimization problem: MIN: X₁ + X₂ Subject to: -4X₁ + 4X₂ ≤ 1 -8X₁ + 12x₂ 2 13 X1 X2 20 (a) What is the optimal solution to this LP problem? (b) Now suppose that X₁ and X₂ must be integers. What is the optimal solution? (X₁, X₂) - (c) What general principle of integer programming is illustrated by this question? O The optimal integer solution to an ILP is not, in general, also a basic feasible solution to the continuous LP. The optimal objective function value of a minimization ILP is always higher than that of the continuous solution. The optimal integer solution to an ILP cannot, in general, be obtained by rounding the continuous solution. The optimal integer solution to an ILP is, in general, also an optimal solution to the continuous LP. O The optimal objective function value of a minimization ILP is always smaller than that of the continuous solution.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the following optimization problem: X1 + X2 Subject to: -4X, + 4X2 s 1 -8X, + 12X, 2 13 X4, X2 2 0 MIN: (a) what is the optimal solution to this LP problem? (b) Now suppose that X, and X2 must be integers. What is the optimal solution? (X, X2) - (c) What general principle of integer programming is illustrated by this question? O The optimal integer solution to an ILP is not, in general, also a basic feasible solution to the continuous LP. O The optimal objective function value of a minimization ILP is always higher than that of the continuous solution. The optimal integer solution to an ILP cannot, in general, be obtained by rounding the continuous solution. The optimal integer solution to an ILP is, in general, also an optimal solution to the continuous LP. O The optimal objective function value of a minimization ILP is always smaller than that of the continuous solution.
Transcribed Image Text:Consider the following optimization problem: X1 + X2 Subject to: -4X, + 4X2 s 1 -8X, + 12X, 2 13 X4, X2 2 0 MIN: (a) what is the optimal solution to this LP problem? (b) Now suppose that X, and X2 must be integers. What is the optimal solution? (X, X2) - (c) What general principle of integer programming is illustrated by this question? O The optimal integer solution to an ILP is not, in general, also a basic feasible solution to the continuous LP. O The optimal objective function value of a minimization ILP is always higher than that of the continuous solution. The optimal integer solution to an ILP cannot, in general, be obtained by rounding the continuous solution. The optimal integer solution to an ILP is, in general, also an optimal solution to the continuous LP. O The optimal objective function value of a minimization ILP is always smaller than that of the continuous solution.
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