  We consider the product knapsack problem, which is the variant of the
classical 0-1 knapsack problem where the objective consists of maximizing the
product of the profits of the selected items. These profits are allowed to be
positive or negative. We show that this recently introduced variant of the
knapsack problem is weakly NP-hard and present a fully polynomial-time
approximation scheme (FPTAS) for the problem. Moreover, we analyze the
approximation quality achieved by a natural extension of the classical greedy
procedure to the product knapsack problem.
