Calculation of maximum values of blocks in space

I actually want to calculate, how to load an HGV with the most carriers of charge. So I basically want to know the maximum value of a specific geometrical form, fitting into another geometrical form. For example: The HGV has the dimensions 13.6 lenght ,2.4 width and 3 hight. The carriers of charge have the dimension of 2.7 length, 1.2 width and 1.4 hight. How can I calculate the maximum value of carriers fitting in the HGV and how can I find out how they have to be loaded. I thought of the Lagrange multiplayer methode but I'm not quite sure how to use it. Thanks for your help!