A three years project on the installation in an Olefins Plant of an on-line Optimizer is described in some details for the following items : Plant Modeling, Plant Constraints, Plant Measures, Data Reconciliation, On-line Optimization, Numerical Approaches and Results. The conclusions drawn by the paper indicate that Plant Optimization is today the main advisory tool for those Plant Operation Managers who aim to reduce costs and increase Plant profit while operating the plant in safe conditions.