(6) Let B2 to be Birkhoff polytope of order 2, that is the collection of all 2 x 2 matrices with nonnegative entries whose rows and columns each sum to one. Suppose Cij are real numbers such that C11 +022 > C12 +021. Consider the following LPP: maximize: C11911 + C12212 + C21221 +222222 subject to: xe B2 111 where x is the 2 x 2 matrix 112 122 221 Find all BFS. Find the maximizer r* and the maximum cost for this LPP. For each of the BFS you found in part (c), find all the basic directions Dj. For the maximizer r*, show that for all basic directions Dj at x* the reduced cost ID; C12 +021. Consider the following LPP: maximize: C11911 + C12212 + C21221 +222222 subject to: xe B2 111 where x is the 2 x 2 matrix 112 122 221 Find all BFS. Find the maximizer r* and the maximum cost for this LPP. For each of the BFS you found in part (c), find all the basic directions Dj. For the maximizer r*, show that for all basic directions Dj at x* the reduced cost ID;