Question: Linear Programming Mechanics

For this unit, we are going to think about the mechanics of Linear Programming.  Your book mentions this fact (page 244):  "The optimal solution to a linear programming problem can be found at an extreme point of the feasible region for the problem."  Explain this statement with an actual example of your own.  Finally, discuss whether you agree with the book's statement.  Why should the optimal solution of any Linear Programming solution be lying at the corner points of the feasible region?  Why must it be at the corner points?

If you agree with this statement, try to come up with your own "simple" explanation of why this is, using words and phrases that most anyone would understand.  If you disagree, then explain an instance in which this might be false.

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