$G(x,y)$= $\max (xk_1+(1-x)\log_2(1+\frac{xyk_2}{1-x}))$,
subject to: $0 \le x \le 1 $, $0 \le y \le 1$,
where $k_1$ and $k_2$ are two positive quantity. Individually it is observed that $G(x,y)$ is a concave function of $x$ when $y$ is kept constant and also it is a concave function of $y$ when $x$ is considered as constant. What will happen when both the constraints are there?