Labor Input and Compost Output Using a Quadratic Production Function

Abstract

This study analyzes the relationship between workforce size and total compost output using a quadratic production function. A descriptive mathematical approach is applied to the function reported in a group project-based learning report on compost production. The coefficients are treated as fixed inputs, and the analysis consists of differentiation, a second-derivative test, and comparison of neighboring integer workforce levels. For the function Q(x) = −0.5x² + 10x, where x represents the number of workers, the maximum total output is 50 production units at 10 workers. Output at both 9 and 11 workers is 49.5 units. Marginal product decreases throughout the model domain, becomes zero at 10 workers, and turns negative beyond that point. Average output at the maximum is 5 units per worker, which is distinct from maximum average labor productivity. The analysis establishes an optimum conditional on the stated function; it does not demonstrate that 10 workers is an empirically validated or profit-maximizing staffing level. Applying the result requires confirmation of the output unit, production period, underlying observations, and model coefficients, alongside assessment of equipment capacity and compost quality.