Unmanned aerial vehicles have shown promise in agriculture and nature management by providing rapid delivery of essential cargo to remote areas that are inaccessible by land transport routes. Given these considerations, an important research area involves modeling the task of creating scenarios for transporting diverse cargoes while accounting for constraints such as route network capacity, shortages of certain types of cargo, unmanned vehicle carrying capacity, and other relevant factors. In a previous study, the authors proposed a model to optimize the transportation plan for heterogeneous car-goes based on cost minimization for a route network of arbitrary structure. The model includes mechanisms to prioritize delivery requests. This work builds upon the previous study and addresses situations where constraints prevent the transportation of the entire volume of cargo intended for delivery. A model is proposed for maximizing the total volume of cargo passing through the route network in such cases. The proposed model is based on a multiproduct maximum flow problem and includes mechanisms to consider the prioritization of cargo delivery requests for different prioritization schemes under lexicographic preferences. An algorithm for finding the optimal plan is described. The experimental study results on modeling the process of cargo delivery to remote areas are presented, including visualization of the simulation results based on a digital terrain model.