The optimal relaxed solution for an ILP has X₁ = 3.6 and X₂ = 2.9. If we branch on X₁, what constraints must be added to the two resulting LP problems? A)X₁$\ge$ 3, X₁ $\ge$ 4 B)X₁ = 4 C)3$\le$ X₁, X₁ $\le$ 4 D)X₁ $\le$3, X₁ $\ge$ 4

Question

Quizplus · Accepted Answer

If we branch on X₁, we create two possibilities: X₁ ≤ 3 and X₁ ≥ 4. For the first possibility (X₁ ≤ 3), we need to add the constraint X₁ F1F1F1S1 ≤ F1F1F10 + 3. This ensures that X₁ is less than or equal to 3, since if it were greater than 3, the constraint would be violated (e.g. if X₁ = 4, then F1F1F1S1 would need to be less than or equal to 0, which is impossible). For the second possibility (X₁ ≥ 4), we need to add the constraint X₁ F1F1F1S1 ≥ F1F1F10 + 4. This ensures that X₁ is greater than or equal to 4, since if it were less than 4, the constraint would be violated (e.g. if X₁ = 3, then F1F1F1S1 would need to be greater than or equal to 1, which is also impossible). Therefore, the correct answer is D.

The Optimal Relaxed Solution for an ILP Has X1 = ≥\ge≥

The Optimal Relaxed Solution for an ILP Has X₁ = $\ge$