For the furniture problem with constraints 2x + y <= 40, x + 3y <= 60, x >= 0, y >= 0 and objective Z = 30x + 60y, the corner points are (0,0), (20,0), (0,20), and the intersection of the two lines. Find the intersection point.

The feasible region (shaded) is bounded by the constraint lines; the fundamental theorem of LPP guarantees the optimal value of the objective function occurs at one of the corner points (O, A, B, C), so only these need to be checked, not the entire region.