We observe that the constraints x≥0,y≥0,x≤5,y≤5 already confine the region to a small square in the first quadrant, so the feasible region is bounded.
This makes (B) true and (A) false.
To find the corner points, we look at the intersections of the boundary lines:
- Intersection of x+y=4 with axes: (4,0) and (0,4).
- Intersection of x+y=8 with x=5: (5,3).
- Intersection of x+y=8 with y=5: (3,5).
- Intersection of x=5 and y=5 is (5,5), but this is outside x+y≤8 (5+5=10>8).
- The actual corner points are: (4,0),(5,0),(5,3),(3,5),(0,5),(0,4).
Counting these points, there are 6 corner points. Therefore, (D) is true.
The correct choice is Option 4: (B) and (D) only.