Accelerator-driven subcritical systems (ADS) rely on an external spallation neutron source to sustain the fission chain reaction. Controlling the spatial distribution of that source is critical to achieving a prescribed power density profile while minimizing source intensity. This project formulates the source distribution problem as a linear programming optimization problem (LPOP), with constraints derived from the required power density distribution in the subcritical assembly. The approach yields optimal source configurations directly, without iterative trial-and-error adjustment, and provides a principled framework for source design in ADS reactor concepts.