The feasible region for the constraints x- y 0, x-5 y -5, x 0, y 0 is shown by the figure:

Step-by-step solution

The constraints define the feasible region through four inequalities: x - y 0 y x x - 5y -5 y 1 5 x + 1 x 0 y 0 The boundary lines are y = x and y = 1 5 x + 1 , intersecting where x = 1 5 x + 1 , yielding 4 5 x = 1 , so x = 5 4 and y = 5 4 . Testing (0,0) shows it violates y 1 5 x + 1 since 0 1 is false. The feasible region lies in the first quadrant, bounded below by y = 1 5 x + 1 and above by y = x , beginning at ( 5 4 , 5 4 ) and extending infinitely rightward. Among the options, only Option C correctly depicts