This is a basic functionality of Linear Program which has to be implemented in Sage. This function could use the functions defined in libraries such as GLPK or CBC.

http://en.wikipedia.org/wiki/Linear_programming

Update:

This old ticket is somewhat vague. Some clarification.

• For simplex-based solvers, there should be facilities for extracting dual information from the optimal dictionary. Some backends already provide functions like get_row_dual (GLPK); LPBackendDictionary - a debugging view of a MIP backend connected to interactive_simplex_method #18804 provides a way to expose this information in a more high-level way.
• For simplex-based solvers, there should be a way to explicitly request using the primal or the dual simplex method. For GLPK, this is possible using solver parameter "primal_v_dual". Other solvers support this too, but I don't think the Sage backends expose it. Ideally, there should be a backend-independent way to request a particular method.

CC: @sagetrac-r-gaia-cs

Component: linear programming

Issue created by migration from https://trac.sagemath.org/ticket/7290