Unformatted text preview: Label these four 1 × 3 vectors y 1 ,y 2 ,y 3 ,y 4 . Give the dual objective function value (as a function of b 1 ) for each of y 1 ,y 2 ,y 3 ,y 4 . Call these functions V 1 ( b 1 ) ,V 2 ( b 1 ) ,V 3 ( b 1 ) ,V 4 ( b 1 ). 4. (a) What do the four functions V 1 ( b 1 ) ,V 2 ( b 1 ) ,V 3 ( b 1 ) ,V 4 ( b 1 ) from part (c) and the Weak Duality Theorem tell you about the function z * ( b 1 )? (b) Draw a ﬁgure as in part (2b) showing all four functions V 1 ( b 1 ) ,V 2 ( b 1 ) ,V 3 ( b 1 ) ,V 4 ( b 1 ), rather than only one. What does this plot reveal about z * ( b 1 )? 5. There are inﬁnitely many dual feasible solutions y for P ( b 1 ). Describe in words a ﬁgure analogous to the ﬁgure in part (4b) that “shows” each of the relevant functions V ( b 1 ), one for each dual feasible solution....
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This note was uploaded on 03/08/2012 for the course ORIE 3300 at Cornell.
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