In this paper we derive optimal state feedback laws for end-point optimization of a dynamic system where the final time is free and the system has a scalar inequality constraint. The existence of a singular region as well as the nature of the state feedback law (static or dynamic) is completely characterized in terms of the system dynamics. Explicit synthesis formulae for the state feedback laws are presented. Once the state feedback laws for end-point optimization have been derived, issues on how these laws can be implemented as part of a closed-loop scheme are discussed. As illustrative examples of application of the proposed methodology, several end-point optimization problems in batch chemical reactors are considered.