What are the key principles of chemical equilibrium, and how do they apply to the industrial synthesis of ammonia via the Haber process? Discuss the roles of temperature, pressure, and catalysts in optimizing the reaction conditions for maximum yield, and explain the impact of these factors on the position of equilibrium according to Le Chatelier's principle. Provide real$-$world examples of how adjustments in these variables are implemented in large$-$scale ammonia production facilities.