The common region of the solution of the ineq | vedclass

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(B) To determine the common region,we analyze the given inequations:$1$. $x+2y \geq 4$: The boundary line is $x+2y=4$. Testing the origin $(0,0)$,we g

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unbounded and non-origin side

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(B) To determine the common region,we analyze the given inequations:$1$. $x+2y \geq 4$: The boundary line is $x+2y=4$. Testing the origin $(0,0)$,we get $0+0 \geq 4$,which is false. Thus,the region is on the non-origin side of the line.$2$. $2x-y \leq 6$: The boundary line is $2x-y=6$. Testing the origin $(0,0)$,we get $0-0 \leq 6$,which is true. Thus,the region is on the origin side of the line.$3$. $x, y > 0$: This restricts the region to the first quadrant.By observing the intersection of these regions,the feasible region is not enclosed by a finite boundary,meaning it is unbounded. Since the region does not include the origin and is defined by the intersection of these half-planes in the first quadrant,it is an unbounded region on the non-origin side. Therefore,the correct option is $B$.

The common region of the solution of the inequations $x+2y \geq 4$,$2x-y \leq 6$ and $x, y > 0$ is

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