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In this exposition a novel feasible version of traditional discretization methods for linear semi-infinite programming problems is presented. It will be shown that each -usually infeasible -iterate can be easily supplemented with a feasible iterate based on the knowledge of a Slater point. The effectiveness of the method is demonstrated on the problem of finding model free bounds to basket option prices which has gained a significant interest in the last years. For this purpose a fresh look is taken on the upper bound problem and on some of its structure, which needs to be exploited to yield an efficient solution by the feasible discretization method. The presented approach allows the generalization of the problem setting by including exotic options (like power options, log-contracts, binary options, etc.) within the super-replicating portfolio.