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1. 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 sj1996)
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.
Duplicate post.
3. (Original post by sj1996)
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.
It's long enough since I did this that I can't remember the definition of a canonical linear programming problem.

That said, I am fairly sure that if you do write down the definition, this is going to be completely obvious, based on the observation that if you have two vectors u, v and a linear functional f, then:

.

Applying this to the objective function and the constraints should suffice.

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