Represent constraints with equations, inequalities, and systems; interpret viable and non-viable solutions in context.
Graph a feasible region from inequalities
Problem
For \(x+y\le~6\), \(x\ge~0\), \(y\ge~0\), identify boundary types, shading directions, and feasible-region vertices in counterclockwise order starting at \((0,0)\).
The feasible region is the overlap of all three half-planes. We’ll first turn each inequality into its boundary and decide whether that boundary is included, then use the nonnegative conditions and a test point to locate the common shaded side. Finally, the intersections of the included boundaries give the region’s vertices in the requested order.
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