Optimize number of cuts of various lengths from a given length

I need some help in finding the best way to determine how many cuts of a variety of sizes can be achieved from a longer length. The goal would be to have the remainder of the longer length as close to zero as possible.

For example...

I have a board at 563.625" long
There are four possible chop lengths to come from that board... 78.3125", 62.625", 86.625" and 55.5"
How many chops of each length can I achieve from 563.625"

Note: I do not have to use all chop sizes from the length of the board. I am looking for varying combinations with minimal loss.