In this paper we consider a nonlinear integer programming problem, arising from educational investments. By introducing a rudimental transformation, we discuss the properties of a set of all solutions to the problem and obtain a sufficient and necessary condition under which a vector is a solution of the problem. By means of the rudimental transformation a method to solve this problem is given. At the end we give an example and discuss the time-complexity of computation for this problem. Using the method in this paper, another problem similar to the above can be solved, for example, that of agricultural investements for planting.