In this work, this system has been solved by the application of the Fourier-Motzkin method, which is based on the transformation of the original system into an equivalent one much simpler to solve. As a result, the quantities each truck has to deliver to the customers are computed, and the system can create the best FTL shippings list. Merging such result with the optimal LTL shipments list previously created, enables to generate the overall optimal shipping list.