Many marketing management models assume that a manufacturer can always supply enough products to meet customer demand. In real situations, however, this is not always true. Demand fulfillment depends on practical factors such as production capacity limits, market uncertainty, and changing supply–demand conditions. Manufacturers cannot simply increase production in direct proportion to demand. Individual customers also cannot directly influence production decisions, but their needs are reflected through retailer orders and overall market feedback. This paper develops a nonlinear supply chain model incorporating realistic manufacturing capacity limits. Under this framework, production volumes do not expand monotonically with shifting consumer demand, necessitating a departure from traditional linear formulations. We evaluate the system’s equilibrium solutions and analyze their stability margins via the Routh–Hurwitz framework. The mathematical analysis indicates that the unchecked system yields unstable trajectories for specific parameter sets. To suppress these variations, we deploy multiple feedback control strategies designed to restore systemic equilibrium. Extensive numerical simulations are presented to verify the operational efficacy and robustness of the proposed stabilization schemes within the modified supply chain framework.