In an LPP, the feasible region represented by the set off constraints $2x + 3y \leq 18$, $x + y \leq 10$, $x \geq 0$, $y \geq 0$ is

The feasible region must satisfy ALL four constraints simultaneously.

Each constraint represents:

$2x + 3y \leq 18$ - points below or on the line $2x + 3y = 18$

$x + y \leq 10$ - points below or on the line $x + y = 10$

$x \geq 0$ - points on or to the right of the y-axis

$y \geq 0$ - points on or above the x-axis

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For line $2x + 3y = 18$:

When $x = 0$:

$3y = 18$

$y = 6$

Point: $(0, 6)$

When $y = 0$:

$2x = 18$

$x = 9$

Point: $(9, 0)$

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For line $x + y = 10$:

When $x = 0$:

$y = 10$

Point: $(0, 10)$

When $y = 0$:

$x = 10$

Point: $(10, 0)$

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Comparing the intercepts:

Line $2x + 3y = 18$ cuts y-axis at $6$ (lower)

Line $x + y = 10$ cuts y-axis at $10$ (higher)

Line $2x + 3y = 18$ cuts x-axis at $9$ (lower)

Line $x + y = 10$ cuts x-axis at $10$ (higher)

Line $2x + 3y = 18$ is more restrictive and creates a smaller region closer to the origin.

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The feasible region satisfying all constraints:

Located in the first quadrant due to $x \geq 0, y \geq 0$

Bounded by the line $2x + 3y = 18$

Vertices: $(0, 0)$, $(9, 0)$, and $(0, 6)$

This triangular region is Region A.

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Region B or C violate the constraint $2x + 3y \leq 18$

Region A ∪ B includes points that don't satisfy all constraints

Therefore, the feasible region is Region A.