Basic information about the task, issues, motives and goals to be achieved are given in the introductory part of this paper. Additionally, all the essential elements covered by the paper are described in a concise way. The second chapter deals in detail with open-end investment funds, as well as the existing categories of these funds. The basic characteristics of open-end investment funds are given, as well as the risks associated with investing in them. The most important features of all categories of these funds, advantages and disadvantages of investing in each category, as well as mutual comparisons are also segments of this chapter. The third chapter gives a theoretical explanation of linear programming, sensitivity analysis and the methods for linear programming problems solving. Simplex method, as the most important method, is elaborated in more details. It is also shown how linear programming can be used in investment decision making. The fourth chapter provides basic information about the LiPS computer program, which is later used to solve the problem. The characteristics and possibilities of the program are listed, as well as the way of working in it. The fifth chapter is the central part of the paper. Problem is explained in details, as well as solving of the problem in stages. Data about the average annual income of the funds in the previous five years were collected and, after sorting, the most successful funds were selected, to which the available money was allocated. Objective and constraints are defined and the model is set. The data from the model were entered into the computer program LiPS, after which the problem was solved. The obtained results are analyzed in details. Part of the chapter is dedicated to the sensitivity analysis of the obtained results. The final part of the paper is reserved for the conclusion, which includes short analysis and review of the results obtained.