Unformatted text preview: (b). Is the LP unbounded? Does it have a ²nite optimal solution? If so what is the optimal z ? Does the LP have multiple optimal solutions? Explain! (Don’t just say “yes” or “no”.) 4). Consider the polyhedron P = { x  x ≥ } . (a). Show that x = is an extreme point of P . (b). Show that any x n = , x ∈ P is not an extreme point. (Recall, x n = means that at least one component of the vector x is not 0. Therefore x n = , and x ≥ does not imply that x > .) (c). What are the extreme directions of P ? Recall, an extreme direction of a set is a direction d that cannot be written as a positive combination of two distinct directions of the set, that is there do not exist directions d 1 and d 2 of the set, d 1 n = d 2 , and α 1 , α 2 > 0 such that d = α 1 d 1 + α 2 d 2 ....
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 Fall '08
 Arkin,E
 Operations Research, Optimization, #, Polytope, Estie Arkin, extreme directions

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