Manufacturing networks are usually composed by several suppliers of intermediate products and several consumers that upgrade these to products. Coordination between the members of the network involves deciding how much intermediate product is going to be exchanged and at which price. In this work, a two-level Lagrangian approach is proposed to find the optimal transfer of intermediates (in terms of flowrates and prices) so that the profits of the actors participating in the network are balanced. The mathematical framework is first discussed for a simple network consisting of one supplier and one consumer, and then extended to multiple suppliers and consumers. A numerical example for a generic chemical process is presented to demonstrate the approach.