The objective of asphalt mix design is to produce a mix with optimal performance using available aggregate stockpiles. Often, this process does not take into consideration aggregate plant stockpile inventories or the cost of aggregate in the mix. This is due to the lack of tools that enable the lab technician or the engineer to optimize the mix for good performance while reducing the cost of aggregate and managing the stockpile inventory levels. The Bailey method provides useful guidance on aggregate gradation selection for optimal performance. This work presents a linear programming model of the asphalt mix design problem. The algorithm is implemented in MATLAB as an Asphalt Mix Design Optimization (AMIDO) program. The program is successfully validated with real-life data. The results show that AMIDO can be used to successfully produce any mix design with known Bailey method ratios. Also, RAP can be included in a design easily by making use of the Bailey method ratios and AMIDO. This work improves the state-of-the-art in asphalt mix design for dense graded mixes and could potentially be modified for other mixes.