Workforce Size and Compost Production Output Using a Quadratic Production Model

Abstract

This study examines the workforce size that maximizes total output in a quadratic model of compost production. The source manuscript attributes the production function to a group report on compost production optimization, but does not provide the underlying observations or coefficient estimation procedure. The analysis therefore evaluates the supplied model rather than estimates an empirical effect of task allocation. The production function is Q(x) = −0.5x² + 10x, where x denotes the number of workers and Q(x) denotes output in unspecified production units. Differentiation gives a stationary point at 10 workers, and the negative second derivative confirms a maximum of 50 units. Direct comparison with 9 and 11 workers, each yielding 49.5 units, confirms the integer solution. Average output at the maximum is 5 units per worker; this does not represent the maximum of average labor productivity. The result is conditional on the supplied coefficients and does not establish a statistically significant effect of division of labor. Field validation requires defined output units, a common production period, workforce records, and information on task allocation and production constraints.