For an assemble-to-order system with a high volume of prospective customers arriving per unit time, we show how to set nominal component production rates, quote prices and maximum lead times for products, and then, dynamically, sequence orders for assembly and expedite components. (Components must be expedited if necessary to fill an order within the maximum lead time.) We allow for updating of the prices, maximum lead times, and nominal component production rates in response to periodic, random shifts in demand and supply conditions. Assuming expediting costs are large, we prove that our proposed policy maximizes infinite-horizon expected discounted profit in the high-volume limit. For a more general assemble-to-order system with arbitrary cost of expediting and the option to salvage excess components, we show how to solve an approximating Brownian control problem and translate its solution into an effective control policy.