In Getting Started with LINGO, we introduced the concept of dual values. The dual values of a solution are the reduced costs of the variables and dual prices on the constraints. We also discussed the useful information that can be obtained from dual values. Unfortunately, in IP models the interpretation of the dual values breaks down. Due to the discreet nature of IP models, the dual values in the solution to an IP model are of no practical use to the average user. Given this, the dual values should be ignored when your model contains integer variables created through the use of @BIN or @GIN.