I'm using the SimplexSolver class directly to solve a linear program, with AddRow, AddVariable and SetCoefficient. This works quite well.
We need to come up with shadow prices now, and I don't see any way to access either the shadow prices or the simplex matrix.
If I set SimpleSolverParams.GetSensitivityReport to true, casting the return of SimplexSolver.GetReport to ILinearSolverSensitivityReport may be the key here. Checking it out.
It looks like ILinearSolverSensitivityReport.GetDualValue returns the shadow price.
Hopefully this saves someone else a merry chase through dotPeek. :-)