From reading online I found someone said that it has a unique optimal solution when $a$ and $b$ are positive and $a \neq b$.
Could someone explain why this is the case?
I know that if $a = b$ then any x,y values that satisfy the equation $x + y = (1/a)$ are optimal, and thus the solution is not unique. But I am confused about how to show that the solution for when $a < b$ and when $a > b$ are unique.