Question: Maximization of a nonlinear function over 2 variables and two parameters

I am trying to maximize a non-linear function f with respect to variables {a,b}.

Could any one suggest a smarter way of entering this into Maple please, as I am not able to get an answer.Thank you.

The function (shown below) also has the parameters {c,H} in it and I have the constraint:

CONSTRAINT:______________0

My Function f:

(256 a^4 (4 c - H) + (1604 c - 10385 H) H^4 -
   60 b^3 H (56 c + 177 H) + 6 b^2 H^2 (-708 c + 1663 H) +
   4 b H^3 (944 c + 1873 H) + b^4 (180 c + 4303 H) -
   256 a^3 (32 b c - 43 b H - 28 c H + 43 H^2) +
   96 a^2 (7 b^2 (4 c + H) + 7 H^2 (-4 c + 17 H) -
      2 b H (16 c + 55 H)) +
   16 a (3 b^2 (100 c - 147 H) H + 3 b (96 c - 61 H) H^2 +
      3 b^3 (40 c + 17 H) + H^3 (-388 c + 445 H)))/(49152 (a -
     H) H (-b + H) (-c + H))