B₂ = {(2₂1 X12 X22 |xij≥0 for i, j = 1, 2, X11 + 12 = 2, X21 + x22 = 2, x11 + x21 = 1.5, x12 + x22 = 2.5 (6) Let B₂ to be the set described in the screenshot attached Suppose cij are real numbers such that C11C22 C12 + C21 > 0. Consider the following LPP: maximize: C11x11 +C12x12 + C2121 + C2222 x11 X12 X21 X22 € B₂ subject to: (a) Write this problem in canonical form {x = (x11, 212, 21, 22) € R4 | Ax = b, x>0}. Hint: A should be a 3 x 4 matrix (after you eliminate one row which is linearly dependent on the others). (b) List all BFS. (c) Which BFS * has the maximum cost for this LPP? For the maximizer r* show that for all basic directions D: at r* the reduced cost.

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