In this study, a new problem that aims to maximize the profit of housing contractors based on the limitations of the contractors is proposed. The budget and the available workforce of the contractor as well as market conditions and the existence of suitable locations can be given as examples of the limitations of the contractors. Formulation of the problem requires estimating the expected costs and the expected profits of the construction alternatives. The limitations on the budget of the contractor and the suitability of the subcontractors may prevent the execution of all the construction opportunities. This situation leads to the problem of selecting the most appropriate housing construction alternatives. The construction opportunities can be executed or not. This forms binary decision variables, and the problem can be solved by simplex or branch-and-bound methods. An additional construction alternative doubles the number of construction combinations that constitute the search domain of the problem. The number of construction opportunities is not expected to be excessive. For this reason, the problem can also be solved by complete enumeration. Three hypothetical housing contractor profit maximization problems are formulated and solved to measure both the computational demand and the ease of application of the simplex, branch-and-bound, and complete enumeration techniques. The comparison revealed that all the techniques provide the optimum result for the problem. Complete enumeration is the easiest technique to implement because of the small search domain of the problem.