How many vertices are in the solution region of (x\leq 5), (y\leq 3), (x+y\geq 4), (x\geq 0), and (y\geq 0)?

Correct answer: (4)

The direct answer is option B, 4 vertices. Begin with the rectangle in the first quadrant: 0≤x≤5 and 0≤y≤3. The condition x+y≥4 keeps the part on or above the line x+y=4. The line meets the top edge y=3 at x=1, giving (1,3), and it meets the bottom edge y=0 at x=4, giving (4,0). The remaining rectangle corners (5,3) and (5,0) also satisfy x+y≥4. Thus the four vertices are (1,3), (5,3), (5,0), and (4,0). Option A, 3, misses one corner. Option B, 4, counts all four boundary turns. Option C, 5, incorrectly counts an intersection that is not a vertex or counts an excluded rectangle corner. Option D, 6, overcounts points along an edge. Remember that a vertex is a corner where the boundary changes direction, not every point on a line.