The present invention provides a system and method for determining the prices and order quantities that maximize a retailer's expected profit by using a multi-dimensional distribution of the highest prices that customers are willing to pay. This is novel, as well in the literature as in the patent database. Brand switching is dealt with, taking into account that consumers who come into the store with a-priori preferences for products build a-posteriori preferences at the point of purchase based on actual retail prices and availabilities in the store.