Haven't looked at your xls or anything but it appears this is really just an optimization problem. What you need to determine is whether your interest function is convex or concave. Knowing this, once you find a stationary point, youre done. That is, defining

, you want to first find a point so that

Then you want to compute the determinant of the Hessian matrix of I at where the Hessian is defined as:

Then you need to study the determinants (leading principal minors) of this matrix.

So compute

=

for ( )

Then check the following:

(a) if is local maximum.

Any local maximum of a convex function is also global maximum.

To test for convexity check whether the HessianH(x)is positive semidefinitex.