In recent years, the Toyota Production System has also assumed in western manufacturing plants a predominant position. Lean Manufacturing, as it is usually called in the occidental world, aims at a “Single-piece-flow” job handling and has its advantages compared to the classic “Batch and Queue” job handling. On the other hand, mathematical Linear Programming optimization techniques have passed into oblivion, having obtained the feel to be inappropriate for production planning. Although the two approaches have different aims and application, they give particular attention to scarce resources. The concepts of “bottleneck” in Lean Manufacturing and “shadow price” in Linear Programming are complementary. The paper shows the different focus of the two approaches and crystallizes their synergic values.