Finding the Feasible Region

Algebra 1 · Axiom Academy

EXAMPLE Finding the Feasible Region Graph a system of linear inequalities and identify the vertices of the solution set. Graph the system of inequalities , , and . Shade the feasible region where all three overlap, then find the vertices (corner points) of that region. The graph shows the three boundary lines and the triangular feasible region where all three conditions are met. The orange dots mark the vertices. Nice work. You graphed a system of three inequalities and found the corner points of its feasible region. Boundary lines: Inequalities with or get solid boundary lines (the boundary is included); inequalities with or get dashed lines (the boundary is excluded). Shading: Each inequality's shaded side is the set of points that satisfy it; the feasible region is where all the shaded regions overlap. A quick test point (like the origin) tells you which side to shade. Vertices: The corner points are found by solving each pair of boundary lines as a system. Here they are , (4, 11) , and (4, -3) . Finding the feasible region and its vertices is the key step in linear programming, where the optimal value of a quantity always occurs at one of these corners.

This is the written version of the interactive lesson above. See the full Algebra 1 course.