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tanotes4 - Some remarks on Assignment 4 Question 1 Ax b 1...

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Some remarks on Assignment 4 Question 1 1. The statement Ax b Ax d x 0 is infeasible” does not imply Ax b x 0 is in- feasible” . (In general, the logical statement “ not ( A and B and C ) ” does not imply “ not ( A and B ) ”.) 2. The dual of max 0 T x s.t. Ax b , Ax d , x 0 is given by min y , z b T y - d T z s.t. A T y - A T z 0 , y 0 , z 0 (not min b T y - d T z s.t. A T y 0 , A T z 0 , y 0 , z 0. See Pg. 35-37 of the printed course notes for the method of constructing duals.) 3. y T b z T b does not imply y z (even if b > 0). 4. a < b does not imply a < 0 < b . Question 7 Majority of the class can answer this question correctly. One common mistake in this question is to pick the pairs ( x 2 , x 1 ) and ( x 5 , x 1 ) in (i) and the pair ( x 5 , x 1 ) in (ii) . They are not valid pairs for the respective questions because they fail the minimum-ratio test (which is necessary for choosing the leaving variable; see Pg.
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