All practical MPC implementations should have a means to recover from infeasibility. We present a recently developed infeasibility handler which computes optimal relaxations of the relaxable constraints subject to a user-defined prioritization, by solving only a single linear program on-line in addition to the standard quadratic programming problem on-line. A stability result for this infeasibility handler combined with the Rawlings-Muske MPC controller is provided, and various practical and computational issues are discussed. From a simulated FCCU main fractionator case study, we conclude that the proposed strategy for designing the proposed infeasibility handler is applicable to the problems of realistic size.