Consider the following primal-dual pair. max (10, -12, -28)x min (2, -8)y 5 10 -2 s.t. 5 - 7 1 4 ) x = (3 ) st 1 y = 12 1 28. X>=0 Y -=0 (a) Write down all the complementary slackness conditions. (No justifications required.) (b) Let x = (0, 0, 2)T . Use the Complementary Slackness Theorem to prove that x is optimal for (P), and determine all possible optimal solutions for (P) and (D). (c) Let c = (10, -12, -28)" , which is the vector of coefficients in (P). Suppose we want to change c while keeping all solutions found in part (b) to remain optimal. Determine all possible c for which this happens