Ethylene is produced from an ethane rich feed. Variations in the feed flowrate and ethane composition are expected. It is important to know whether the existing plant can operate in the feasible region for the expected deviations. In particular, the questions raised in this work are how much feed can be processed in the plant and how can plant bottlenecks be detected in order to increment plant capacity. For a given feed, the operating conditions of the ethylene plant are evaluated solving a lion linear programming problem. The objective function is the profit maximization and the feasible region is limited by the design specifications and equipment capacities. Active constraints related to equipment capacities indicate plant bottlenecks. A numerical example is presented for a real ethylene plant where the feed flowrate and ethane composition vary within expected ranges. Bottlenecks are detected in two sectors of the plant : in the furnaces and in the ethylene-ethane splitter. Possible solutions to overcome the bottlenecks are also studied.