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This book is a work for a PhD Mathematics, from Mathematics Department, Modibbo Adama University of Technology, Yola, Nigeria. It deals with the optimal control of a one-machine multiple-product manufacturing system with setup changes, operating in a continuous time dynamic environment. The system is deterministic. When production is switched from one product to the other, a known constant setup time and a setup cost are incurred. Each product has specified constant processing time and constant demand rate, as well as an infinite supply of raw material. The problem was formulated as a feedback control problem. The optimal solution provides the optimal production rate and setup switching epochs as a function of the state of the system (backlog and inventory levels). For the steady state, the optimal cyclic schedule was determined. To solve the transient case, the system's state space was partitioned into [n(n-1)/2], where n is the number of products, mutually exclusive regions such that with each region, the optimal control policy was determined analytically. From the result of analysis, a number of useful recommendations were made. The book is relevant in manufacturing Industries