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Optimal solutions in linear programming

Explain the following statement with an example: the optimal solution to a linear programming problem can be found at an extreme point of the feasible region for the problem.

Do you agree with the following two questions?
1. Why should the optimal solution of any Linear Programming solution be lying at the corner points of the feasible region?
2. Why must it be at the corner points?

Do you agree or diagree the statement above? Why or why not? If you do not agree, please explain an instance in which this might be false.

Thank you

Solution Preview

Yes, this statement is true. This is because parallel objective function lines move towards larger objective function values without entirely leaving the feasible region. Therefore, any feasible solution on ...

Solution Summary

Solution uses example to explain a statement regarding linear programming. Also provides detailed response, with diagrams, to explain a few questions.