Anyway my solution is tedious, but it works. Let me know if you have a problem somewhere.
We repeatedly use .
let us first put -----------(1)
and then ----------------(2)
We want to know the maximum value of
But we can use (1) and (2) above to reduce W to
Now set and
Our simplified conditions now read....
This is simple.... :P
The maximum value is 4
(and it occurs for X=Y=2, further you can substitute it above and find the values for which this happens.However the question does not demand the numbers but only the maximum)
I have left a little bit for you, in particular getting . Try it!