The graph with correct feasible region of L.P.P. for the constraints 2 x+ y 10, y x, y 2, x, y 0 is

Step-by-step solution

The feasible region is the intersection of all constraint inequalities: 2x + y 10 , y x , y 2 , x 0 , and y 0 . The boundary lines include 2x + y = 10 through (0,10) and (5,0) , y = x through the origin, and y = 2 horizontally. The origin (0,0) satisfies all constraints, confirming the region lies below or on each line in the first quadrant. The vertices occur at intersections: (0,0) , (5,0) from y=0 and 2x+y=10 , (4,2) from y=2 and 2x+y=10 , and (2,2) from y=2 and y=x . These four points form a quadrilateral entir