Inequalities created by relating gauge (distance) functions and their dual support functions have been used in economics and operations research/management science to measure efficiency and productivity. The most familiar example is the Farrell (1957) measure of cost efficiency and its...

In this note we show that the diet problem and the benefit-of-the-doubt (BoD) aggregation are linear programming duals. That is, the primal (dual) formulation of the diet problem is equivalent to the dual (primal) formulation of the BoD model as long as food prices are set equal to one. In...