The optimized sizing of flotation banks is investigated analytically. A solution is presented here for the optimum allocation of cell capacities to stages of a counter-current flotation plant, subject to a fixed total of cell capacities. The paper uses "enrichment functions" to facilitate the analysis. The optimization technique gives a simple and exact solution for the case where the concentrations of streams can be characterized adequately by scalar values. The methods can also apply to the general case with concentration vectors, for which the more intricate analysis has not yet been completed The solution of the scalar version gives some insight into the general case and a simple adaptation might give a first approximation of the general solution.