$ G (x, y) = xk_1 + (1-x) log_2 (1+ frac {xyk_2} {1-x}) $,

subject to: $ 0 le x le 1 $, $ 0 le and le 1 $,

where $ k_1 $ Y $ k_2 $ They are two positive quantities. Individually it is observed that $ G (x, y) $ is a concave function of $ x $ when $ and $ remains constant and is also a concave function of $ and $ when $ x $ It is considered as constant. What will happen when both restrictions are there?