IE220_F08_hw3sol

# IE220_F08_hw3sol - IE220: Introduction to Operations...

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IE220: Introduction to Operations Research Fall 2008 Prof. Imre P´olik Homework 3 Solutions 1) 6.1-10 (6 points) If the primal problem is infeasible, then the dual is either unbounded or infeasible. This means that if you pick some infeasible problem, then the dual is not guaranteed to be unbounded, you might have to try several primal problems, before you hit one whose dual is unbounded. On the other hand, the dual of an unbounded problem is always infeasible. Thus, you can start from the dual side, ﬁnd an unbounded problem, then take its dual to get the primal infeasible problem. Remember, the dual of the dual is the primal. The easiest way to create an unbounded problem is to graph it, then read out the inequalities. (There are a lot of good answers here.) 2 4 6 2 4 x 1 x 2 x 1 4 x 1 2 max x 2 max x 2 x 1 2 x 1 4 x 1 ,x 2 0 The primal (dual dual) problem is clearly infeasible: min - 2 y 1 + 4 y 4 - y 1 + y 2 0 0 y 1 + 0 y 2 1 y 1 ,y 2 0 1

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## This note was uploaded on 11/03/2008 for the course IE 220 taught by Professor Storer during the Spring '07 term at Lehigh University .

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IE220_F08_hw3sol - IE220: Introduction to Operations...

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