Problem 4: The following subproblems are independent from one another. Recall that, given c E Rn, A E Rmxn and b E Rm, one may define the primal and dual linear programs (P) : maxTERn c 'x s.t. Ax =b and x > 0 (D) : minyERm by s.t. Ary > c whose optimal values satisfy val(P)