The following statements are either true or false. If true provide a proof. If false provide a counter example. Assume Y is non empty. You may use the aid of diagrams. i. Every technologically efficient production plan is on the boundary of Y . ii. Every production plan y Y that lies on the boundary of Y is efficient. iii. If Y is convex and exhibits the no free lunch property, then it exhibits non increasing returns to scale. iv. If Y exhibits non increasing returns to scale, then it exhibits irreversibility. v. If Y exhibits constant returns to scale, then it is convex. vi. If Y exhibits non decreasing returns to scale, then it is violates the no free lunch property.