Finish this statement: The objective function value for ILP problems can never. match the optimal solution to its LP relaxation. be better than the optimal solution to its LP relaxation. be as poor as the optimal solution to its LP relaxation. be worse than the optimal solution to its LP relaxation.

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**Question:** Finish this statement: The objective function value for ILP problems can never...

- ○ match the optimal solution to its LP relaxation.
- ○ be better than the optimal solution to its LP relaxation.
- ○ be as poor as the optimal solution to its LP relaxation.
- ○ be worse than the optimal solution to its LP relaxation.

**Explanation of Concepts:**
- **ILP (Integer Linear Programming):** A mathematical optimization problem where some or all variables are constrained to take integer values.
  
- **LP Relaxation (Linear Programming Relaxation):** This is the process of relaxing the integer constraints of an ILP, allowing the variables to take any non-integer values, making the problem easier to solve. 

The question is testing the understanding of the relationship between the solutions to ILP and its LP relaxation, which is a fundamental concept in optimization theory.
Transcribed Image Text:**Question:** Finish this statement: The objective function value for ILP problems can never... - ○ match the optimal solution to its LP relaxation. - ○ be better than the optimal solution to its LP relaxation. - ○ be as poor as the optimal solution to its LP relaxation. - ○ be worse than the optimal solution to its LP relaxation. **Explanation of Concepts:** - **ILP (Integer Linear Programming):** A mathematical optimization problem where some or all variables are constrained to take integer values. - **LP Relaxation (Linear Programming Relaxation):** This is the process of relaxing the integer constraints of an ILP, allowing the variables to take any non-integer values, making the problem easier to solve. The question is testing the understanding of the relationship between the solutions to ILP and its LP relaxation, which is a fundamental concept in optimization theory.
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