Social Law Synthesis (SLS) in strategic environments is a novel multi-unit mechanism design problem, spanning modeling to computational challenges. We derive a method to specify the problem succinctly, reduce payment determination to allocation determination, and design an integer linear programming (ILP)-based algorithm that further reduces allocation to a polynomial-time ILP formulation. This offloads intractability to powerful ILP solvers, yielding a truthful, individually rational, and profit-optimal mechanism.