For the LPP Maximize Z = 5x + 4y subject to 3x + y <= 12 and x + 2y <= 10, x,y >= 0, the corner points include (0,0), (4,0), (0,5), and the intersection of the two boundary lines. Find Z at that 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.