Abstract

This paper examines the 2 – dimensional optimization theory, its problems and solutions. Lots of work exist in literature studying the one - dimensional optimization theory and its problems / solutions. Hence, our attention is squarely on 2-dimensional optimization theα^0ory and its problems but we are often challenged by these questions - are they solvable and if the response is in the affirmative, then are the solutions produced unique? In the course of our study, we established that the 2-dimensional optimization problem is solvable, that is a 2 – dimensional optimal control problem is solvable, by providing proofs to some logical assertions. Furthermore, we also showed that the solutions generated from these problems - the optimal control problems are unique and prove the optimality of the solution obtained by checking J(α)≥J(α^0) for anyα∈G_T (V). These findings provide and encourage avenues for the application of 2 – dimensional optimization models in the industrial sector.