The feasible region is the convex hull of the given corner points.
For (1/2, 13/2): y = 6.5 is above max y = 5, so outside region.
For (1/2, 5/2): On line from (0,4) to (2,5), at x=0.5, max y = 4.25; y = 2.5 lies inside.
For (5/2, 5): At x = 2.5, the upper boundary from (2,5) to (6,3) gives y = 4.75; y = 5 is outside.
For (5, 5): At x=5, max y = 3.5 on boundary; y = 5 is outside.
Only (1/2, 5/2) lies in the feasible region.