The feasible region formed by the constraints :
\( x+y\le 40,x\le 10,y\le 40,y\ge 2x,x,y\ge 0 \) is a
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Trapezium
For \( 0\le x\le 10 \) the region lies between the line y = 2x (below) and the line x + y = 40, i.e. y = 40 − x (above). Since \( 40-x\le 40 \) for x ≥ 0, the constraint \( y\le 40 \) is automatically satisfied and adds no edge.
Corner points:
\( \displaystyle x=0,\ y=2x:\ (0,0) \)
\( \displaystyle x=0,\ x+y=40:\ (0,40) \)
\( \displaystyle x=10,\ x+y=40:\ (10,30) \)
\( \displaystyle x=10,\ y=2x:\ (10,20) \)
The region has four corners, O(0, 0), (0, 40), (10, 30), (10, 20). Its sides on x = 0 and x = 10 are both vertical, hence parallel, while the other two sides (on x + y = 40 and y = 2x) are not parallel. A quadrilateral with exactly one pair of parallel sides is a trapezium.