In Exercises 3 and 4 solve the given integer programming problem by the cutting plane method and sketch the graph of the set of feasible solutions and the cutting planes 3. Maximize 2 = x + y subject to 2x + 3y < 12 2x + Y < 6 X20, y 2 0, integers . Maximize z = x + 4y subject to x + 6y < 36 3x + 8y < 60 x20, y 2 0 integers_ In Exercises 5-12 solve the given integer programming problem using the cutting plane algorithm: 5_ Maximize z = 4x +y subject to 3x + 2y < 5 2x + 6y < 7 3x + Ty < 6 x20, y 2 0, integers .