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Cell suppression and audit programs have been used at the Census Bureau for many years for insuring the confidentiality of establishments that contribute data that are used for building economic magnitude data tables. Since the 1987 Economic Census, the suppression programs were based on network flow models which work well for 2D tables but which have some drawbacks for higher dimensional tables. Linear programming (LP) based models now appear to be a practical option for higher dimensional tables and they do not have these same drawbacks. This paper describes work over the last two years in implementing these LP models, as well as some of the mathematical reasons for preferring the LP based models. Practical aspects of these programs are discussed; e.g., calculating capacities, refinement runs, backtracking, linked tables, frozen cells, and rounded data. A description of earlier work is also included, as are goals for future research.