Linear programming selection of internal financial laws and a knapsack problem

We formulate and solve explicitly a linear programming problem that arises from the problem of choosing an internal financial law of a given financial project such that the associated discount vector maximizes a linear objective function. If the original problem has optimal solutions, then it is equivalent to a knapsack problem. We obtain its basic optimal solutions in closed form. After considering the special case of nonnegative preference directions, we also obtain a new characterization of the existence of internal financial laws.