The feasible region represented by the constraints \( 2x+y\le 12,x+2y\le 12,4x+5y\ge 20,x,y\ge 0 \) of LPP is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Region B
Testing each inequality at the origin O(0, 0):
\( 2x+y\le 12 \): \( 0\le 12 \) is true, so the region is on the side of \( 2x+y=12 \) containing O.
\( x+2y\le 12 \): \( 0\le 12 \) is true, so the region is on the side of \( x+2y=12 \) containing O.
\( 4x+5y\ge 20 \): \( 0\ge 20 \) is false, so the region is on the side of \( 4x+5y=20 \) away from O.
With \( x,y\ge 0 \) the region is in the first quadrant, below both lines \( 2x+y=12 \) and \( x+2y=12 \), and above the line \( 4x+5y=20 \).
Region A lies below \( 4x+5y=20 \), region C lies beyond \( 2x+y=12 \), and region D lies above \( x+2y=12 \). Only region B satisfies all the constraints.
It is bounded by the corner points (5, 0), (6, 0), (4, 4), (0, 6) and (0, 4).