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    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.
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    (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.
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    (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:

    f(\lambda u + (1-\lambda)v) = \lambda f(u) + (1-\lambda) f(v).

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