We have :
Find the maximum value of A
Find x, y and z when A=max value.
(Remember the category)
(In reply to Most of a solution
by Brian Smith)
There are two maximum points on A. They are given by y=4/sqrt 31 and y=-4/sqrt 31. These are the only maxima on the curve A.
x=7/sqrt 31 y=4/sqrt 31 z=20/sqrt 31 A=8
x=-7/sqrt 31 y=-4/sqrt 31 z=-20/sqrt 31 A=8
This has been confirmed by solving dA/dy for all cases.