This article gives necessary and sufficient conditions for the existence of a finite maximum of a quadratic functional. The functional is the present value of a revenue stream in discrete time over an infinite horizon. Both scalar and vector versions of the problem are solved. It is shown that the problem always has a solution for a sufficiently high finite discount rate. Some conditions to ensure the nonnegativity of the solution are also presented. The origin of the problem is finding the sequence of outputs that will maximize the present value of the net return of a monopolist who sells k related products with related demands described by a set of k nth order linear difference equations.