I remember studying mathematical optimization techniques for computers way
back in engineering school, so I remember some of the concepts. It is clear
to me that you cannot have step functions or other non-continuous functions
in the model, because that causes the search to get lost.

Basically, at each point, the technique is to take a small step in the
direction of each independent variable, then calculate the "slope" (partial
derivative of F with respect to X) of the function. Then the next point is
calculated by moving all independent variables in the appropriate
direction. If you have any functions in your cells that return the same
result (say 0) when this small step is taken, then the slope appears to be
0, so the technique concludes (wrongly) that it is at the "top of the hill"
(maximization problem) and then stops.

You simply have to take all of the non-continuous functions out of your
model (i.e. ROUND, ROUNDDOWN, ROUNDUP, RAND,
IF(var1<0,SomeValue,OtherValue), etc.).

I believe that Solver really is a powerful tool and can be used in a lot of
situations, as long as you understand the setup and usage requirements
first.

I guess the other lesson (or rule) is: Always double-check your
presentation demos before class! (You always get questions that can test
your credibility anyway!)
--
Regards,
Bill Renaud