*What are you trying to optimize?*

Neither. It's one of

- If he has an unlimited number of tapes: Minimize the number of tapes needed (bin packing problem).
- If he has an limited number of tapes: Maximize the value of what will fit on the tapes he has (multiple knapsack problem).

*Efficiently fill drives of fixed size? The latter is (as AppleFritter points out) the knapsack problem. *

No, it's not, as I already pointed out. In the knapsack problem, you have one bin (tape), and you're trying the maximize what you can put on it. Stuff is left behind.

Comment onRe^2: Computer science Problem - single dimension bin packing