🚀 go-pugleaf

 About 12 years ago, I helped my sister with a problem like this, only
it was a matter of maximizing the weight. I didn't need a computer and
didn't have one. Just by simple fiddling, I was able to figure
out how to get just 5 grams under an allowable limit of 20 tonnes. This
also took into account how they would all physically fit in the container.

Unfortunately, a mathematical solution to this apparently mathematical
problem overlooks some practical difficulties: (1) if the people who actually
have to do the work of packing the stuff into the container have to learn
something special or complicated in order to load the stuff into the container
according to the optimal solution, it is not going to happen. (2) The
specifications of the boxes, both their sizes and weights, are subject to
variations, often because of variations in their manufacture, sometimes
because of stupid reasons such as moisture absorbed by the cardboard.
(3) If the variations, which are not known, or the failure of the workers to
conform to the actual solution, cause one to exceed the constraints
of the problem (in your case, the dimensions of the container, in my sister's
case, the allowed weight), then that is a serious problem (in your case, it
won't fit, in my sister's case, there would be a fine).

The difficulty of taking into account variations in the parameters of the 
problem or constraints in the work practices of the people who load the 
container, when no one has ever bothered to collect that information, seems 
to argue against seeking a mathematical solution of the problem. Instead,
it seems like a better idea to tinker together a solution which is 
somewhat less than optimal and simply to ask someone in authority in the 
company  if that solution is good enough for their purposes. If they insist 
on pushing the limits of the problem, explain you can deliver better
solutions if necessary, but you need detailed information about the
factors I mentioned above.

Allan Adler
ara@altdorf.ai.mit.edu