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(B) To determine the linear constraints,we analyze the half-planes defined by each line for the shaded region:$1$. For the line $3x + 4y = 18$,the ori

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$3x + 4y \leq 18, 2x + 3y \geq 3, x - 6y \leq 3, -x + 2y \leq 2, x \geq 0, y \geq 0$

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(B) To determine the linear constraints,we analyze the half-planes defined by each line for the shaded region:$1$. For the line $3x + 4y = 18$,the origin $(0,0)$ satisfies $3(0) + 4(0) = 0 \leq 18$. Since the shaded region contains the origin relative to this line,the constraint is $3x + 4y \leq 18$.$2$. For the line $2x + 3y = 3$,the origin $(0,0)$ gives $2(0) + 3(0) = 0 \leq 3$. Since the shaded region is on the side away from the origin,the constraint is $2x + 3y \geq 3$.$3$. For the line $x - 6y = 3$,the origin $(0,0)$ gives $0 - 0 = 0 \leq 3$. Since the shaded region is on the side containing the origin,the constraint is $x - 6y \leq 3$.$4$. For the line $-x + 2y = 2$,the origin $(0,0)$ gives $0 + 0 = 0 \leq 2$. Since the shaded region is on the side containing the origin,the constraint is $-x + 2y \leq 2$.$5$. The region is in the first quadrant,so $x \geq 0$ and $y \geq 0$.Thus,the correct set of constraints is $3x + 4y \leq 18, 2x + 3y \geq 3, x - 6y \leq 3, -x + 2y \leq 2, x \geq 0, y \geq 0$.

The shaded area in the figure below is the solution set for a certain linear programming problem. The linear constraints are given by:

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