Suppose that we have a linear program

(a) write down the dual to this auxiliary problem.

(b)explain why...

(c)assume that th einitial LP is infeasible...

Problem 3. Suppose that we have a linear program a Maximize 2 subject to A55 :1 l3, if 2 D. If the initial dictionary is infeasible [exactly when E 2 O), we'd start with \"Phase 1\" of the simplex method by working with an auxiliary problem which we could put into matrix notation as a It'faxirnize2*:gsubjectto[1'1t1][;_;.JI ] gimmizu. Here the notation [ 1 i A ] means that we take A and augment on a column of 1's to the left. (3) Write down the dual to this auxiliary problem. (b) Explain why the initial problem being infeasible is equivalent to the existence of 5* with ATS; 2 0, j? Z 0, and l3 - 37