Algorithm Needed for covering a non-rectangular shape with rectangles

Algorithm Needed for covering a non-rectangular shape with rectangles

I have a set of 5 types of rectangles (pieces of cloth):
66x96
81x96
90x102
108x102
1110x102
I can use as many or as few as I want. these rectangles need to be placed
next to, or on top of, each other to form the shape below:
____________________
| 300 |
|132 |
_____| |_____
| 132 132 |
|108 |108
|_____ _____|
| |
|132 |
|____________________|
300
they can overlap if needed (which means they would get cut), and may go
outside of those bounds (again, they would be cut), but in the end, they
must fully cover the defined area. The goal is to have as few cut pieces
as possible.
This is different than most packing algorithms in that the shapes being
packed can be mutated, and the area being filled needs to be completely
filled.