Project portfolio selection involves decision making and it plays a crucial role in any organization. Therefore selecting not just the right projects but also the right mix of projects for the portfolio is considered as one of the most important tasks for organisations to ensure the achievement of the corporate strategy within limited resources and capabilities of the organization. Prioritizing and selecting optimal project portfolio can be very challenging especially with a large number of projects with multiple constraints and interdependences. In an ideal world with unlimited budget the project selection process would be very straightforward. However, this is not the case in life situations. In this work, an attempt is made to address this challenge. An integer linear programming model for project selection was developed and applied in a selected organization in Nigeria. The model seeks to optimize the mix of the projects to be undertaken while keeping the total cost and project interdependency as constraints. The analysis of the results showed that a total of 11 projects out of 16 were eligible for selection in the period under review. The total cost of the selected project was 92,840,000 Naira, which was about 90% of the total budget. Ordinarily, apart from not prioritizing and obtaining an optimal project mix, the community would have spread its entire resources on the 16 projects with some of them being abandoned later. The model can also be used to plan an optimal mix of project portfolio for a future date within the limitations of a given set of constraints and interdependence.