The region represented by the inequations 2x | vedclass

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(D) To find the feasible region,we analyze the given constraints:$1$. $2x + 3y \leqslant 18$: This represents the region on or below the line $2x + 3y

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null set

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(D) To find the feasible region,we analyze the given constraints:$1$. $2x + 3y \leqslant 18$: This represents the region on or below the line $2x + 3y = 18$. The intercepts are $(9, 0)$ and $(0, 6)$.$2$. $x + y \geqslant 10$: This represents the region on or above the line $x + y = 10$. The intercepts are $(10, 0)$ and $(0, 10)$.$3$. $x \geqslant 0, y \geqslant 0$: This restricts the region to the first quadrant.Comparing the two lines:For $2x + 3y = 18$,the maximum $x$-value is $9$ and the maximum $y$-value is $6$.For $x + y = 10$,the minimum $x$-value is $10$ and the minimum $y$-value is $10$.Since the region defined by $2x + 3y \leqslant 18$ lies entirely below the line $x + y = 10$ in the first quadrant,there is no point $(x, y)$ that satisfies both $2x + 3y \leqslant 18$ and $x + y \geqslant 10$ simultaneously.Therefore,the feasible region is a null set.

The region represented by the inequations $2x + 3y \leqslant 18$,$x + y \geqslant 10$,$x \geqslant 0$,$y \geqslant 0$ is

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