Evaluating marginal costs associated with ratio and other constraints in linear programmes

In certain applications of linear programming, such as blending problems, there are constraints which place limits on ratios of linear combinations of the decision variables. These constraints can easily be linearized, but the values of the dual variables associated with them give the marginal cost associated with the linearized and not the original constraint. This note shows how the required marginal cost can be calculated by considering the problem as a special case of a more general one.