Determine whether the statement is true or false. Justify your answer.
1. If an objective function has a maximum value at the vertices (4, 7) and (8, 3), then it also has a maximum value at the points (4.5, 6.5) and (7.8, 3.2).
2. If an objective function has a minimum value at the vertex (20, 0), then it also has a minimum value at (0, 0).
3. If the constraint region of a linear programming problem lies in Quadrant I and is unbounded, the objective function cannot have a maximum value.