Consider the following instance of the 0-1 knapsack problem: maximize x1 + 8x2 + 12x3 + 16x4 + 17x5 + 22x6 + 24x7 subject to 2x1 + 4x2 + 5x3 + 13x4 + 14x5 + 15x6 + 22x7 31 xi {0, 1} i = 1, . . . , 7 Solving the linear relaxation on this initial problem returns an optimal solution of (0, 1, 1, 0.538, 0, 1, 0). Based on this, which of the following inequalities represent effective cutting planes that will remove the current optimal solution to the linear relaxation from the feasible region without removing integer feasible points? Write "Cutting plane" or "Not cutting plane" and explain why for each part. (a) x3 + x6 + x7 2 (b) x3 + x5 + x6 2 (c) x3 + x4 + x6 2 (d) x2 + x3 + x4 + x5 2 (e) x4 + x5 + x6 2 (f) x1 + x2 + x3 + x4 4 (g) x1 + x2 + x3 + x4 2