The feasible region, graphed by representing inequalities x - y ≤ 7, x ≥ 0, and y ≥ 0, is the shaded area where all conditions overlap, forming a polygon on the coordinate plane.
To graph the feasible region defined by x - y ≤ 7, x ≥ 0, and y ≥ 0, we can start by representing each inequality on a coordinate plane.
The first inequality, x - y ≤ 7, can be rewritten as y ≥ x - 7. This inequality represents a boundary line where the area above it is the feasible region. The second inequality x ≥ 0 indicates that the feasible region is to the right of the y-axis, and the third inequality y ≥ 0 means it is above the x-axis. Combining these, we can shade the region that satisfies all three conditions.
The feasible region is the intersection of the shaded areas created by these three inequalities. It is the region where x and y values satisfy all conditions simultaneously. Typically, this region forms a polygonal shape.