The input-output structural analysis is a valuable tool when designing economic policies since it allows us to know which are the most important linkages and sectors of an economic system. The coefficients' sensitivity analysis is one of the major approaches of the structural analysis. With it we may measure how the output is influenced by changes in the coefficients. However, the classical sensitivity analysis, based on the Sherman & Morrison formula, shows several limitations. In this paper, an alternative approach based on linear programming and that deals with such challenges is proposed. The technique is then applied to an employment analysis in nine European countries.