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(C) Let's analyze the shaded region and its linear constraints:$1$. Looking at the graph,the region is bounded by the lines $y=x$ and $-x+3y=3$,along

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$x-y \geq 0, -x+3y \leq 3, x \geq 0, y \geq 0$

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(C) Let's analyze the shaded region and its linear constraints:$1$. Looking at the graph,the region is bounded by the lines $y=x$ and $-x+3y=3$,along with the axes $x=0$ and $y=0$.$2$. The shaded region is situated below the line $-x+3y=3$. Testing the origin $(0,0)$,we get $-0+3(0) = 0 \leq 3$,which satisfies the inequality. Thus,the constraint is $-x+3y \leq 3$.$3$. The region is situated to the right of the line $y=x$ (or below the line $y=x$ in terms of $y$-values for a fixed $x$). Testing a point in the region,such as $(2, 0)$,we have $x-y = 2-0 = 2 \geq 0$. Wait,let's re-evaluate: for the region to the right of $y=x$,we have $x \geq y$,which means $x-y \geq 0$.$4$. Re-checking the graph: The shaded region is bounded by $y=x$ on the left and $-x+3y=3$ on the top. For points in the region,$x \geq y$ (so $x-y \geq 0$) and $-x+3y \leq 3$. $5$. Comparing with the options,option $(C)$ matches these conditions: $x-y \geq 0, -x+3y \leq 3, x \geq 0, y \geq 0$.

For the following shaded region,the linear constraints are:

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