Solving Problem

I have a total number of cubic meters (CBM), and need to figure out the best
combination of shipping containers that leaves the least amount left over.
Here is an example:

Total CBM = 311

Container Type 20' holds max of 28 CBM
Container Type 40' holds between 55 and 58 CBM
Container Type 40H holds between 65 - 68 CBM
Container Type 45 holds max of 75 CBM

To further complicate this, I would like to minimize the number of 45'
containers, and also have an alternative solution that doesn't involve using
20' containers. I've tried using Solver, but can't seem to get things set up
right to make it work.

Thanks in advance!