One of the key factors of competitiveness of developing industrial enterprises in modern conditions is sustainable development of enterprises in the long term, particularly, through rational allocation of enterprise resources during investment of relevant projects. At the same time, traditional approaches to finding the optimal amount of investments (involving marketing research and subsequent break-even analysis) for projects for developing industrial enterprises only yield results with relatively low adequacy, as it is difficult to provide objective source data when economic processes cannot be modeled in a continuously changing environment. This article focuses on mathematical methods and models as alternative tools for solving problems connected to determining the optimal amount of investment. We have developed an analytical model of return on investment as a function of its initial volume (as the main parameters of investment projects in the field of industrial enterprise development) based on the Verhulst model. This analytical model was used to find the main characteristics of implementation of investment projects in the field of developing industrial enterprises, including the minimum and maximum amounts of rational investment, as well as extreme amounts of income and losses from investing in industrial enterprise development projects. We have developed a procedure for substantiating the characteristics of industrial enterprise development. The procedure is based on applying analytical and optimization modeling tools as part of modern specialized software environments. The developed procedure has been implemented on a practical example: assessment of characteristics for investment in civil engineering projects in terms of the initial amount of invested funds and the corresponding return, using the computing capacities of Microsoft Excel software, particularly, the Solver add-in for implementing various optimization models. Implementation of the proposed procedure lead us to conclude that the obtained results were highly adequate and, as a sequence, the developed procedure had a high practical importance.