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(D) Given the system of linear inequations:$1) 2x + 3y \leq 18$$2) x + y \geq 10$$3) x \geq 0, y \geq 0$For the first inequation $2x + 3y \leq 18$,the

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an empty set.

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(D) Given the system of linear inequations:$1) 2x + 3y \leq 18$$2) x + y \geq 10$$3) x \geq 0, y \geq 0$For the first inequation $2x + 3y \leq 18$,the boundary line is $2x + 3y = 18$. The intercepts are $(9, 0)$ and $(0, 6)$. Since the origin $(0, 0)$ satisfies $2(0) + 3(0) \leq 18$,the feasible region lies towards the origin.For the second inequation $x + y \geq 10$,the boundary line is $x + y = 10$. The intercepts are $(10, 0)$ and $(0, 10)$. Since the origin $(0, 0)$ does not satisfy $0 + 0 \geq 10$,the feasible region lies away from the origin.Comparing the two regions: the first region is below the line passing through $(9, 0)$ and $(0, 6)$,while the second region is above the line passing through $(10, 0)$ and $(0, 10)$. These two regions do not intersect in the first quadrant $(x \geq 0, y \geq 0)$.Therefore,there is no common region that satisfies all the given inequations. Thus,the feasible region is an empty set.

The feasible region represented by the inequations $2x + 3y \leq 18$,$x + y \geq 10$,$x \geq 0$,$y \geq 0$ is

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