The solution set of the constraints |x-y| 1, x, y 0 is

Step-by-step solution

The constraint |x-y| 1 can be expressed as the compound inequality -1 x-y 1 , which yields x-1 y x+1 . Combined with the non-negativity conditions x 0 and y 0 , the feasible region lies between the parallel lines y = x-1 and y = x+1 in the first quadrant. For any x 1 , there exists a y satisfying x - 1 y x + 1 and y 0 . As x increases without bound, such y values also grow without bound, making the solution set unbounded. The correct choice is B .