Each of the following ILPs has no feasible solutions. Solve the corresponding LP relaxation graphically and indicate whether your relaxation results are sufficient to show that the ILP is infeasible.

(a) min 10x1 + 15x2 s.t. x1 + x2 Ú 2

-2x1 + 2x2 Ú 1 x1, x2 = 0 or 1

(b) max 40x1 + 17x2 s.t. 2x1 + x2 Ú 2 2x1 - x2 … 0 x1, x2 = 0 or 1

(c) min 2x1 + x2 s.t. x1 + 4x2 … 2

-4x1 + 4x2 Ú 1 x1 Ú 0, x2 = 0 or 1

(d) max 57x1 + 20x2 s.t. x1 + x2 Ú 4 x1 = 0 or 1 0 … x2 … 2