The Answer
If you set N=2, and ri0=ri1=ri for each i, and set R=12?i?[L]ri, then the feasibility of this linear program is precisely the Partition problem. Namely, a feasible solution chooses for each i?[L] either xi0 or xi1, so that summing the ri for those i for which you chose xi0 equals R, and similarly for 1.