After some plotting, like
Plot3D[F[d, n], {d, 0, 8}, {n, 0, 1/2},
PlotRange -> {-1, 2500000}]
I come to suspect that the maximum is attained near d=4
and n=1/100
. Using these values as starting points I get
In[172]:= FindMaximum[F[d, n], {{d, 4}, {n, 1/100}}]
Out[172]= {1.94398*10^6, {d -> 4.00704, n -> 0.0125096}}
I don't know if these are sensible values for your problem.