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Given a structured system with variable size and transitions at the end of each period, the paper's objective is to determine the optimum proportions of admission to obtain a given relative distribution in each grade or level of the system. The model used is markovian determinist and proportions of transition are time-homogeneous. Polygonal approximations are introduced to solve the non-linear program. A complete numerical illustration is included. [ABSTRACT FROM AUTHOR]

The article presents mathematical research and an algorithm for solving linear programs with variable binaries. This research was based on the prior work of E. L. Lawler and M. D. Bell. The algorithm which is presented is based on the idea of monotonically increasing functions and uses many of the properties of this type of function, according to the author. The article presents several mathematical examples and notes the uniqueness of this approach to solving linear programs with variable binaries. According to the author, this approach eliminates about 40% of vectors that were previously necessary in order to derive solutions to an auxiliary problem that is necessary to the solution of many linear programs with variable binaries. The author mentions questions for further research.