With the primal objective value, I know the dual objective value. I also know the right hand sides of the original program. However, I don't know the values of the dual variables at the optimal point. Is there an easy way to determine those values once the solution to the primal is found (instead of having to resolve the dual from scratch)?
Most of the solvers for LP have some kind of way to get the dual variables directly. See my post here http://blog.mosek.com/2014/03/working-with-dual-in-practice.html for the MOSEK solver.