What is the shape of the region formed by (x\ge 1), (x\le 5), (y\ge 0), and (y\le 4)?

Correct answer: rectangle

The inequality x≥1 places the region on or to the right of the vertical line x=1, while x≤5 places it on or to the left of x=5. Together these give the vertical range from x=1 to x=5. Similarly, y≥0 gives the region on or above the horizontal line y=0, and y≤4 gives the region on or below y=4. Their combination has both a fixed horizontal width and a fixed vertical height.

The boundary lines meet at the four points (1,0), (5,0), (1,4), and (5,4). Since all four boundary inequalities are inclusive, the boundary is included, producing a closed rectangle. It is not a triangle because there are four sides, not an unbounded strip because both coordinates are bounded, and not empty because points such as (3,2) satisfy every inequality. Therefore option C is correct.