This paper is concerned with optimal feedback control synthesis for periodic processes with economic control objectives. The focus is on tube-based methods which optimize over robust forward invariant tubes (RFITs) in order to determine the nonlinear feedback law. The main contribution is an approach to conservatively approximating this set-based periodic feedback control optimization problem by a tractable optimal control problem, which can be solved with existing optimal control solvers. The approach is applied to an uncertain periodic biochemical production process, where the objective is to maximize the profit subject to robust safety constraints.