hw2 - x cannot be an optimal solution to this LP 3 Consider...

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AMS 540 / MBA 540 (Fall, 2010) Estie Arkin Homework Set # 2 Due in class on Thursday, September 23, 2010. 1). (a) Show that the set of all feasible solutions to the following linear program forms a convex set: min { cx | Ax = b, x 0 } (b) Prove that the set of optimal solutions to the linear program (of part (a)) forms a convex set. 2). Consider the linear program: Minimize cx subject to Ax b, x 0, where c is a non zero vector. Suppose that a point x 0 is such that Ax 0 < b and x 0 > 0. Show (prove) that
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Unformatted text preview: x cannot be an optimal solution to this LP. 3). Consider an LP: ( p 1 and p 2 are given constants.) max z =-p 1 x 1 + p 2 x 2 x 1-x 2 = 0 ≤ x 1 , x 2 ≤ 1 (a). What are the extreme points and extreme directions of this LP? (b). Write the equivalent LP in terms of the extreme points and extreme directions. (c). Now suppose that p 1 > p 2 . What is the optimal solution to the LP? (Make sure to state z as well as x 1 , x 2 .)...
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