Hw5_Sol - Math464 - HW 5 Due on Thursday, Feb 18 1 Linear...

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Unformatted text preview: Math464 - HW 5 Due on Thursday, Feb 18 1 Linear Optimization (Spring 2010) Brief solutions to Homework 5 1. As seen in class (in Lecture 11), there may be some change of variables when we convert a polyhedron in general form to standard form. In particular, an unrestricted variable is replaced by two non-negative variables. This transformation inherently creates corner points. For example, the polyhedron represented by { x R 2 | x 2 = 1 ,x 2 } ( x 1 unrestricted in sign) is the open horizontal line lying one unit above the x-axis. This polyhedron has no corner points. But when you convert the same to standard form, you get a positive quadrant (flat plain closed on two edges) in R 3 , with the point (0 , , 1) as a corner point (assuming x 2 is the third variable in the standard form). 2. (a) Let y be an element of the cone C . Consider the polyhedron P = { = ( 1 ,..., n ) R n | n X i =1 i A i = y , i } ....
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Hw5_Sol - Math464 - HW 5 Due on Thursday, Feb 18 1 Linear...

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