The optimal control policy for the maximization of the secreted heterologous protein in a fed-batch bioreactor was obtained using SEY2102 as a model host yeast and SUC2-s2 as a model secretory protein. A dynamic model for host cell growth, gene expression, and the secretion of expressed polypeptides was formulated. The optimal system trajectory contains multiple singular arcs that are distinct from one another. Optimal control requires transitions between these singular arcs. Optimal transitions between multiple singular arcs with bounded controls are uniquely located in observance with the Minimum Principle of Pontryagin. An iterative numerical search strategy for determining the optimal control showed successful convergence properties.