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2. Consider the following LP P: 29 -15621 + 22802 683 subject to: CI Consider three P-feasible solutions: x7 = (2,3, 4)", x = (8, 8, 7) and x2 = (2,5, 11)". a) Find the value of every slack variable of P for the solution x. b) Evaluate the objective function for each of the three solutions (i.e. compute c x , cox and c"'x"). (c) Using just the information in (b), answer one of YES, NO, MAYBE to each of the following questions. Make sure to justify each answer. i. Is x an optimal solution of P? ii. Is x an optimal solution of P? (d) Find a real number a > 0 such that x = x to(x -x'), and xll = x -o(x-x" ) are both P-feasible. (To understand where these equations come from, see the proof of Workout 2.1.3.) (e) Evaluate cox" and cox". (f) Using the information found in (e), what can you conclude, if anything, about the optimality of x