The feasible region represented by the constraints \( x + y \leq 50, 3x + y \leq 90, x \geq 0, y \geq 0 \) of an LPP is:

Region A

The correct answer is Option (3) → Region A

Feasible Region: The feasible region is the quadrilateral ABCD enclosed by the following lines:

• $x + y \le 50$ → line passing through $(0,50)$ and $(50,0)$
• $3x + y \le 90$ → line passing through $(0,90)$ and $(30,0)$
• $x \ge 0$ → right of the $y$-axis
• $y \ge 0$ → above the $x$-axis

From the graph:

Region A (shaded triangular-like region with vertices at $(0,0)$, $(30,0)$, $(20,30)$, and $(0,50)$) satisfies all the constraints.

Hence,

The feasible region is Region A