In the given figure, feasible region represented by the constraints $4x + y \geq 80$, $x + 5y \geq 115$, $3x + 2y \leq 150$, $x,y \geq 0$ is

The constraints are $4x + y \geq 80$, $x + 5y \geq 115$, $3x + 2y \leq 150$, and $x,y \geq 0$.

Each constraint defines a region in the coordinate plane.

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For $4x + y \geq 80$:

The boundary line is $4x + y = 80$

Testing the origin $(0,0)$: $4(0) + 0 = 0 \geq 80$ is false.

The feasible region is on the opposite side from the origin (above the line).

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For $x + 5y \geq 115$:

The boundary line is $x + 5y = 115$

Testing the origin $(0,0)$: $0 + 5(0) = 0 \geq 115$ is false.

The feasible region is on the opposite side from the origin (above the line).

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For $3x + 2y \leq 150$:

The boundary line is $3x + 2y = 150$

Testing the origin $(0,0)$: $3(0) + 2(0) = 0 \leq 150$ is true.

The feasible region includes the origin side (below the line).

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For $x, y \geq 0$:

The feasible region is in the first quadrant.

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The feasible region satisfies all constraints simultaneously:

• Above the line $4x + y = 80$
• Above the line $x + 5y = 115$
• Below the line $3x + 2y = 150$
• In the first quadrant

The intersection of these regions forms a bounded polygonal region.

Based on the constraint directions, the feasible region is Region C.

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Therefore, the answer is Option 3 (Region C).