As a direct result of economic pressures to cut expenses, as well as the legal obligation to reduce emissions, companies and businesses are seeking ways to use energy more efficiently. Trigeneration systems (CHCP: Combined Heating, Cooling and Power generation) allow greater operational flexibility at sites with a variable demand for energy in the form of heating and cooling. This is particularly relevant in buildings where the need for heating is restricted to a few winter months. In summer, the absorption chillers make use of the cogenerated heat to produce chilled water, avoiding waste heat discharge. The operation of a simple trigeneration system is analyzed in this paper. 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. A linear programming model provides the operational mode with the lowest variable cost. A thermoeconomic analysis, based on marginal production costs, is used to obtain unit costs for internal energy flows and final products as well as to explain the best operational strategy as a function of the demand for energy services and the prices of the resources consumed.