Peaks in renewable electricity generation and consumer demand are desynchronized in time, posing a challenge for grid operators. Industrial demand response (DR) has emerged as a candidate for mitigating this variability. In this paper, we demonstrate the application of DR to an air separation unit (ASU). We develop a novel optimal production scheduling framework that accounts for day-ahead electricity prices to modulate the grid load presented by the plant. We account for the dynamics of the plant using a novel dynamic modeling strategy, which allows us to formulate the corresponding optimization problem as a mixed integer linear program (MILP). Further, we present a new relaxation scheme that affords fast solutions of this MILP. Extensive simulation results show significant reductions in operating costs (that benefit the plant) and reductions in peak power demand (that benefit the grid).