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In this paper we develop details of implementation techniques for simultaneous implicit representation of both Simple Upper Bounds (SUB’s) and Variable Upper Bounds (VUB’s) in the simplex method. More precisely, we show how the standard data structures and techniques connected with the SUB simplex algorithm can be extended to deal with VUB inequalities. There is also discussed obtaining of feasibility as it turns out that the standard SUB composite algorithm fails in the VUB case and some special modifications are necessary,