This paper develops a supply allocation model under nonlinear marginal costs. Using a Lagrange multiplier approach, we derive closed-form allocation rules and validate them through scenario-based simulations. Results confirm the cost-threshold effect: low-cost regions supply first, while high-cost regions require policy support or demand growth for activation. The framework not only provides insights for supply management but also extends the theoretical foundation of allocation under nonlinear escalation, with potential applications to transport networks and multi-period planning.