Hi, I'm new to Mathematica. I have the function:

f[x_,y_] =  a1 (1 - (b1/(b1 + c f1 x))^(r1/r2)) + 
 a3 (1 - (b3/(b3 + c f3 (1 - x - y)))^(r5/r6)) + 
 a2 (1 - (b2/(b2 + c f2 y))^(r3/r4))

The unknowns are x and y, where the rest (a1, a2, ..., b1, ... ) are known variables, greater than 0, in the domain of Real numbers. I need a way to find x and y, for which (given we know the other variables) f(x,y) will have the maximum value. When I use the function maximize it takes forever to compute or sometimes it won't even execute. Finding derivatives works but then I need to express x and y in terms of the known variables, however using solve for solving the system of dfdx and dfdy yet again takes forever or doesn't execute at all. Am I approaching this in the wrong way?