In the paper, the authors propose a variant of the mathematical model for justifying the optimal ratio of researchers of different categories to conduct scientific research of the highest possible quality in conditions of limited resources. The discrepancy is formulated between the quality of scientific research and the restriction on financial resources, that is, the problem of resource allocation is solved. The relationship between the quality of scientific research and the number of researchers is proposed to be reflected by the canonical parabola equation. A mathematical model is formulated that reflects the essence of the question under study. The problem is solved using the method of Lagrange multipliers. The results of the study are confirmed by a numerical experiment. Resource constraints have always existed. This is especially true now for the development of the Armed Forces of Ukraine and increasing their combat and mobilisation readiness, which result in the country's defence capability as a whole. Limited funding also takes place in military science. It is very difficult to introduce new full-time positions and divisions. Previously, the number of researchers was justified following regulatory documents when creating scientific institutions and divisions, or by analogy with similar scientific institutions. In other words, the problem was solved empirically or situationally. This scientific study concerns substantiating the number of scientific personnel in conditions of limited resources, taking into account the work that is now performed and will be performed in the future.