This article presents an in-depth case study that demonstrates (i) how the process and control design, involving both discrete and continuous decisions, can be simultaneously optimized for systems described by realistic dynamic models and that (ii) mixed-integer dynamic optimization problems, involving thousands of differential -algebraic equations, can now be solved using state-of-the-art algorithms and technology. The study in question involves a distillation column that is subject to time-varying disturbances and time-invariant uncertainty. A new, multicomponent, mixed-integer dynamic distillation model is developed and used to simultaneously determine the number of trays, feed tray location, column diameter, reboiler and condenser surface areas, 5 x 5 control structure, PI-gains, reset times, and set-points, to obtain an economically optimal system that is also guaranteed to give feasible dynamic operation over all uncertainty scenarios.