This paper considers the properties of an optimal production schedule for a multi-product firm, where the economics of production include employment smoothing costs. The results extend the findings of [Lippman, Steven A., Alan J. Rolfe, Harvey M. Wagner, John S. C. Yuan. 1967. Optimal production scheduling and employment smoothing with deterministic demands. Management Sci. 14 127-158.], which treated only a single product. The analysis establishes bounds on optimal production schedules for both individual products and aggregate work force. The paper also relates monotonicity in each product's demand with monotonicity of production for each item in an optimal schedule.