I have an optimization problem where I need to calculate the maximum of the following function $$ f(x,y,z) = (2^{xy}{z \choose y})^{z+1} $$ where $$ (z+1)(a+y(\lceil{\log_2{(z+1)}}\rceil+x))\leq C $$
$a,C$ are constants.
$a,x,y,z$ are all positive integers.
Using approximations is allowed. Just need to get close.
I have had mathematical analysis courses, but this is beyond me. Would be great if somebody showed their work or walked me through the process. I'm here to learn.