The feasible region of the inequalities x+y l | vedclass

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(D) To find the feasible region,we analyze the inequalities $x+y \leq 1$ and $x-y \leq 1$.$1$. The line $x+y = 1$ passes through $(1, 0)$ and $(0, 1)$

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All the four

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(D) To find the feasible region,we analyze the inequalities $x+y \leq 1$ and $x-y \leq 1$.$1$. The line $x+y = 1$ passes through $(1, 0)$ and $(0, 1)$. The region $x+y \leq 1$ includes the origin $(0,0)$ and extends into all four quadrants.$2$. The line $x-y = 1$ passes through $(1, 0)$ and $(0, -1)$. The region $x-y \leq 1$ also includes the origin $(0,0)$ and extends into all four quadrants.$3$. Since both inequalities represent half-planes that extend infinitely in various directions and contain the origin,their intersection (the feasible region) is an unbounded region that spans across all four quadrants of the Cartesian plane.Therefore,the correct option is $D$.

The feasible region of the inequalities $x+y \leq 1$ and $x-y \leq 1$ lies in $\ldots \ldots \ldots$ quadrants.

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