Abstract In marginal analysis, there is a tendency to overlook the problems of fixed costs. In multi-product firms, however, there are many possible fixed costs. Such firms attempting to optimize profit under capacity constraints must take into account not only their gross margin but also net profit, i.e., profit after incurrence of various alternative fixed charges. Hirsch and Dantzig proposed the original integer programming solution to the "fixed charge" problem and their approach applies directly to product profitability analysis. Their algorithm is demonstrated in a marketing example and the imputations for accountants of this application of operations research technique are discussed.