Mathematics

Problem

When graphing the inequality

x \ge 0

with no restriction on

y

, the feasible region is a) the right half‐plane but excluding the

y

–axis (

x>0

) b) the right half-plane including the

y

–axis c) only the first quadrant (

x\ge0,\,y\ge0

) d) the upper half-plane including the

x

–axis

Intuitive explanation

The key insight is recognizing that " $x \ge 0$ with no restriction on $y$ " describes a vertical half-plane, not a single line. Since $y$ can be anything (positive, negative, or zero), every point satisfying the inequality forms an entire vertical strip. You're shading everything to the right of and including the $y$ -axis—a region, not a boundary.

Intuitive explanation

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