Two new algorithms are proposed for the problem of positioning a new product in attribute space in order to attract the maximum number of consumers. Each consumer is assumed to choose the existing or new product closest to his ideal point according to the Euclidean norm. The first algorithm is based on finding a finite number of intersection points of indifference surfaces. The second algorithm proceeds by considering sets of balls bounded by indifference surfaces and finding points belonging to the largest weighted number of them. Problems with up to 500 consumers groups, 40 existing products and 20 attributes are solved exactly.