Problem #4 (20 points) - Using Primal/Dual Pairs a.) (10 points) Construct the dual of the following LP problem max 2: = OTX + eTy (Objective Function) s.t. Ax + Ay = O (m Constraints) Iy S e (n Constraints) x, y 2 0 (211 Sign Restrictions) where e is an n X 1 vector having all positive entries (228., e > 0), O is the vector/matrix of all 0's, I is the n X n identity matrix and A is an m X 71 matrix and x and y are the decision variables. b.) (10 points) Prove that the optimal solution of the LP is part (a) is zero if and only if ATV > O for some m X 1 vector v. Hint: Note that if ATV > O for some m X 1 vector v, then AT(/\\V) > O for all A > 0