The region represented by the system of inequalities $x, y ≥0, y ≤6, x + y ≤3$

is a bounded region in the first quadrant

The correct answer is Option (1) → is a bounded region in the first quadrant

Constraints: x≥0, y≥0 ⇒ first quadrant.

x+y≤3 ⇒ region lies below the line x+y=3 with intercepts (3,0) and (0,3).

y≤6 is redundant since y≤3 already from x+y≤3 and x≥0.

Intersection is a triangle with vertices (0,0), (3,0), (0,3) ⇒ bounded in first quadrant.

Answer: is a bounded region in the first quadrant.