Can you use linprog? If you split an item 60-40, would that be acceptable? If not, then linprog is not possible.
This is essentially a binary integer linear programming problem. Use intlinprog, with INTEGER variables (vector x) from the set [0,1].
So minimize the product f*x, such that f*x>=sum(f)/2.
To be honest, it is just as easy to use exhaustive enumeration here. All possible sets are given by
dec2bin(0:2^14-1) - '0'
Choose the row that satisfies your goal, which will require all of one matrix*vector multiply, followed by a quick test.
This seems too much probably homework though, so I'll go no further.
