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# Linear Programming Problem watch

1. Hi, could anybody help with a proof for the following linear programming problem.

Prove, in general, that any line segment connecting two distinct optimal solutions of a canonical linear programming problem is an optimal solution. Deduce that any canonical linear programming problem has either zero, one or inﬁnitely many optimal solutions.
2. (Original post by sachin2896)
Hi, could anybody help with a proof for the following linear programming problem.

Prove, in general, that any line segment connecting two distinct optimal solutions of a canonical linear programming problem is an optimal solution. Deduce that any canonical linear programming problem has either zero, one or inﬁnitely many optimal solutions.
May be able to help. Where are you stuck?
3. On all of it
4. (Original post by sachin2896)
On all of it
First off you need to sort out what form does a solution on the line segment joining two optimal solutions look like?

You then need to show that it's optimal.

And that it satisifies the constraints.

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Updated: November 10, 2015
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