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(D) To determine the linear constraints,we analyze the boundary lines of the shaded region:$1$. The line passing through $(3, 0)$ and $(0, 2)$ is $2x

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$2x + 3y \geq 6, 3x + 6y \leq 18, x - 3y \leq 3, -x + 2y \leq 2, x \geq 0, y \geq 0$

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(D) To determine the linear constraints,we analyze the boundary lines of the shaded region:$1$. The line passing through $(3, 0)$ and $(0, 2)$ is $2x + 3y = 6$. Since the shaded region is away from the origin,the constraint is $2x + 3y \geq 6$.$2$. The line passing through $(0, 3)$ and $(6, 0)$ is $3x + 6y = 18$. Since the shaded region is towards the origin,the constraint is $3x + 6y \leq 18$.$3$. The line passing through $(3, 0)$ and $(0, -1)$ is $x - 3y = 3$. Since the shaded region is towards the origin,the constraint is $x - 3y \leq 3$.$4$. The line passing through $(0, 1)$ and $(2, 2)$ is $-x + 2y = 2$. Since the shaded region is towards the origin,the constraint is $-x + 2y \leq 2$.$5$. Since the region is in the first quadrant,$x \geq 0$ and $y \geq 0$.Thus,the correct constraints are $2x + 3y \geq 6, 3x + 6y \leq 18, x - 3y \leq 3, -x + 2y \leq 2, x \geq 0, y \geq 0$.

The shaded region in the following figure represents the solution set for a certain linear programming problem. The linear constraints for this region are given by:

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