This is an analysis type question.

Both the question and the solution are shown below. My inquiry is related to the SOLUTION shown below.

1. How is0?2x2?x?6=(2x?3)(x+2) obtained from5?x2+y=x2+(2?2x?)

Both underlined in RED below in the solution shown

2. How does5?x2+y=x2+(2?2x?) satisfied with?3/2?x?2 ?

Underlined in BLUE.

3. How is1?y?7/4 obtained ?

Underlined in GREEN

4. Explain why the solution states "Thus, as the values ofx andy are bounded (above and below) on D"

Underlined in ORANGE

Please explain clearly showing each step as thoroughly as possible.

If you are using hand-written notes, then please ensure they are tidy and legible as untidy written notes are difficult to interpret. Alternatively use LaTeX.

QUESTION

Consider the mixed constraint optimisation problem of minimising the function f : R2 -> R given by f(x, y) = x2 + y over the set D = {(x, y) ER? | x + 2y = 4, x2 + y