Trigeneration is the combined production of heating, cooling and power from the same source of energy. In this paper, the operation of a simple trigeneration system is analyzed. The system is interconnected to the electric utility grid, both to receive electricity and to deliver surplus electricity. For any given demand required by the users, a great number of operating conditions are possible. The operational mode with the lowest variable cost is obtained through a linear programming model. Three different approaches to determine the costs of internal flows and final products of the simple trigeneration systems are presented: marginal costs corresponding to optimal operation, costs obtained when production costs are distributed to the final products according to their market prices, and internal costs corresponding to a thermoeconomic analysis of the operation mode of the system. As expected, the costs obtained with the approaches mentioned are different and it can be concluded that there are no general rules to decide which approach is best: it depends on the issue under investigation.