In many different development projects, we need to minimize construction costs and usable area according to the design constraints assigned to each project. The aim of the research is to contrive a mathematical model for calculating the dimensions and sizes of rooms in a residential plan to get the least cost and manage the resources of construction. This paper presents a mathematical model (nonlinear programming) to achieve the above-mentioned goals according to the various design constraints and conditions, depending on the nature of the project and the goal of its establishment. To check the efficiency and accuracy of results the system of the nonlinear objective function and nonlinear constraints are solved using Mathematica and GAMS programs in two different cases. Tables and graphical representations of the results are very useful to the problem stated in this study. The study was applied to one of the projects of the New Urban Communities Authority in Egypt.