Given the existing and forseeable oceanic data base, it is argued that practical determination of the general circulation of the oceans is probably impossible. Instead, by using a simple box model as an example, it is shown that mathematical models exist to determine both the range of possible solutions and the extreme values of important properties of all solutions. The specific techniques applied are linear and quadratic programing which are special cases of the more general techniques of optimization theory or mathematical programing. In addition, we provide an example of the use of a general nonlinear inversion technique for solving the problem. The methods should be adaptable to box models in much wider context and to much more elaborate diagnostic models.