For the Linear Programming Problem feasible region shown in figure , for this constraints are
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( x+2y\ge 4,\ x+y\ge 3,\ x\ge 0,\ y\ge 0 \)
The line \( x+2y=4 \) meets the axes at (4, 0) and (0, 2). The line \( x+y=3 \) meets them at (3, 0) and (0, 3).
The origin is not in the shaded region. At the origin \( x+2y=0\lt 4 \) and \( x+y=0\lt 3 \), so the shaded region is on the other side of both lines:
\( \displaystyle x+2y\ge 4,\qquad x+y\ge 3 \)
The two lines meet at (2, 1). The lower edge of the shaded region runs along \( x+y=3 \) from (0, 3) to (2, 1), then along \( x+2y=4 \) from (2, 1) to (4, 0), and the region extends upwards and to the right from there.
The region lies in the first quadrant, so also \( x\ge 0 \) and \( y\ge 0 \).