For an upcoming client project, I'm looking to do a 3D variant on the knapsack problem. Basically, there's a bin of dimensions $x,y,z$, and I have $K$ units of an item with dimensions $a,b,c$. (Assuming rectangular prisms for both the bin and the item).
I want to find the max number of units ($\le K$) that will fit in the bin. Are there are any ready-made Python or R packages I could use for this? Answering this question is actually a preparatory step in a larger optimization model, so even if I need to just write the MIP into the overall model that would be OK too.