Calculus Applications in Optimising Profit Functions for Cassava Processing Enterprises in Taraba State

This study applies differential calculus to the optimisation of profit functions for cassava processing enterprises operating in Taraba State, North East Nigeria, a predominantly agricultural state where cassava cultivation and processing constitute a significant source of rural household income. The study frames the profit maximisation problem for representative processing firms in terms of production cost functions, revenue functions, and the determination of output quantities that maximise profit under competitive and monopolistically competitive market structures. Data on production costs, output prices, and processing capacities are collected through structured questionnaires administered to 45 registered cassava processing enterprises in the Jalingo, Wukari, and Bali local government areas. Total cost functions are estimated using ordinary least squares regression on the collected data, and profit functions are derived by subtracting estimated cost from revenue. Differential calculus techniques, including first and second derivative tests, are applied to identify profit-maximising output levels, and the results are compared against actual production levels reported by surveyed firms to quantify foregone profits arising from sub-optimal production decisions. Results indicate that 62 percent of sampled enterprises produce below the calculated profit-maximising output, with the gap attributable to working capital constraints and market access limitations. The study recommends value chain financing mechanisms and cooperative processing arrangements to enable smaller enterprises to approach optimal production scales. Keywords: differential calculus, profit optimisation, cassava processing, cost functions, Taraba State