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Q: Does deleting a non-binding constraint change optimal solution? If yes, give an example. If no, Prove it.

My try so far:
I read some articles. Some of them mentioned something called shadow price. But, i don't want that because i don't know the meaning of it. I want some explanation with drawing and examples.
Links:
https://books.google.com/books?id=nDYz-NIpIuEC&pg=PT275&lpg=PT275&dq=delete+non-binding+constraint+change+optimal+solution&source=bl&ots=qMnTYhphBo&sig=18Y9YeHzkoybNxY0VYOGhUorB-4&hl=en&sa=X&ved=0ahUKEwjO2tqCg47SAhVICMAKHQr5CBIQ6AEIQjAH#v=onepage&q=delete%20non-binding%20constraint%20change%20optimal%20solution&f=false https://fisher.osu.edu/~croxton.4/tutorial/sensitivity/rhs8.html

Note: I'm completely new to linear programming. I know how to find the solution of a LP-Model just by drawing.

Note: I'm asking this question about linear programming. I read an article which said in non-linear programming, the answer is yes.

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    Why negative point!? :O – 2017-02-13
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    Maybe you can name the articles, so that others understand your question better. – 2017-02-13
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    @GNUSupporter ok i make edit – 2017-02-13
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    While the title and opening line of the body of your Question raise a topic that has been discussed here before, the recent Edits tend to create an impression that you have little experience with solving Linear Programs, and that the significance of "non-binding constraint" is poorly understood. – 2017-02-14

1 Answers 1

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No, it doesn't. Binding constraints are used to "cut out" a polyhedron - the feasible region. Non-binding constraints can be removed without affecting the shape of the polyhedron.

To find a solution, one needs to consider the edges of the polyhedron. In general, there can be infinitely many solutions along an edge.

Now, if the value is maximized along a given edge, then it is also maximized at the vertice(s) of that edge. Linear programming uses this fact and also that there are only finitely many vertices in a given polyhedron. So then algorithms evaluate vertices one-by-one until they reach a point where no further improvement can be found.