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Unformatted text preview: ISE 536Fall03: Linear Programming and Extensions September 3, 2003 Lecture 3: Geometry, Basic Feasible Solutions Lecturer: Fernando Ord onez 1 Examples of LP Geometry Let us construct examples of LPs which have bounded feasible region and single solution bounded feasible region and multiple solutions unbounded feasible region and multiple solutions unbounded feasible region and unbounded objective function value infeasible feasible region Optimum seems to be always in a corner. In this class we will make this precise. 1 1.1 Effects of Transformation on the Geometry Consider the problem min z = x 1 x 2 s . t . x 1 + x 2 1 x 1 ,x 2 Always have the same general shape? 2 Notation Polyhedron: P = { x < n  Ax b } Polytope: A bounded polyhedron. S is a convex set iff for all x,y S and any [0 , 1], x + (1 ) y S ....
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 Spring '05
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