Virtual power plants are a useful tool for integrating distributed resources such as renewable generation, electric vehicles, manageable loads, and energy storage systems under a coordinated management system to obtain economic advantages and provide ancillary services to the grid. This study proposes a management system for a residential virtual power plant that includes household loads, photovoltaic generation, energy storage systems, and electric vehicles. With the proposed management system, the virtual power plant is economically optimized (as in commercial virtual power plants) while providing ancillary services (as in technical virtual power plants) to the distribution grid. A genetic algorithm with appropriate constraints is designed and tested to manage the energy storage system and the charge/discharge of electric vehicles, with several economic and technical objectives. Single-objective optimization techniques are compared to multi-objective ones to show that the former perform better in the studied scenarios. A deterministic gradient-based optimization method is also used to validate the performance of the genetic algorithm. The results show that these technical targets (usually reserved for larger virtual power plants) and economic targets can be easily managed in restricted-sized virtual power plants.