The question is about cutting planes and valid inequalities. I just want to know how to provide all cutting planes for x bar and justify why, and how to prove that the inequality given in the question b is valid for IP. Thank you for your help.

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(a) Consider the following integer program. max (-2,-1,0,0,0)x subject to 1 % 1 0 0 g g g 0 1 0 as: 8 1 0 0 1 g :1: Z O, a: integer. Let 1% = (O, 0, %, 8, 9T Provide all cutting planes for i: that you can generate from the equality constraints above, and briey justify why they are cutting planes for in (15 marks) (b) Consider the following integer program (IP). max cTa; subject to Am 3 b a: 2 D, m integer. For a vector (1 6 IR", [02] is the vector obtained from a by taking the oor of all its entries, for instance [(24, 3, 1.3)Tj = (2,3, 2)T. Let y 2 0 be an arbitrary xed vector and consider the inequality, lyTAJx S lyTbJ- (T) Prove that (T) is valid for (IP); i.e., every feasible solution to (IP) satises (1')