I have a two queries related to the solution given for the below question.

1. Please show in more detail how

x2+y2?2??x??2?and?y??2?

2. Please explain in more detail why D is bounded

Please explain clearly showing each step as thoroughly as possible. If you are using hand written notes, then please ensure they are neat and legible, as it is difficult to interpret illegible hand-written notes. Alternatively, use LaTex.

The question is

Consider the following inequality constraints optimisation problem maximise f(x, y, z) = xy + 2xz +2yz, for D = {(x, y, z) ER3 | 222