You had forgotten Fby, try it:

solve({Ax, Ay, Bx, By, Cx, Cy, Dx, Dy, Ex, Ey}, [F1, F2, F3, F4, F6, F7, Fdx, Fdy, Fey, Fby]);

I am so grateful for your help. It does work great. I was testing the following loop to obtain the plot, but does not sound appropriate, since it is more time-consuming procedure.

with(Optimization);
P := Matrix(n);
M := proc (a, b) options operator, arrow; Maximize(f(a, b, t), t = 0 .. Pi) end proc;
for i to n do
for j to n do
x := .1*j;
y := 1+.1*i;
z := M(x, y);
 P[i, j] := [x, y, z[1]] ;
end do ;
end do;
P1 := convert(P, Array);
pointplot3d(P);