2. {10 marks} consider a generic lp (p) in sef. max{cx : ax = b, x > 03. we previously mentioned a certificate of unboundedness, that is, if there exist a feasible solution ī and a vector d such that ad=0,d > 0,c7d > 0, then (p) is unbounded. the goal of this question is to prove the converse of this, that is, if (p) is unbounded, then such a certificate must exist. we start by considering the following linear program (p') using d as the variable. max{cid : ad = 0,d > 0}. suppose (p) is unbounded. (a) write down the dual (d) of (p), and the dual (d') of (p'). (b) prove that (d) and (d') are both infeasible. (c) prove that (p') is unbounded. (d) prove that there exist a feasible ī and a vector d such that ad = 0,> 0, cd > 0.