Optimasi Produksi Perusahaan Semen dengan Pendekatan Fungsi Turunan: Studi pada PT Semen Indonesia Tbk

Abstract

This study aims to analyze the application of derivative functions in optimizing production at PT Semen Indonesia Tbk. Using a differential calculus approach, the research examines the relationship between revenue, cost, and profit through the concepts of Marginal Revenue (MR) and Marginal Cost (MC). The financial report shows total sales of 33.8 million tons, revenue of IDR 34.95 trillion, and cost of goods sold of IDR 24.54 trillion. The results indicate an average price of IDR 1,033,000 per ton and a variable cost of IDR 726,000 per ton. With a demand elasticity of ε = −2, the analysis yields MR = IDR 516,500 and MC = IDR 726,000 per ton. The optimal production level is calculated at approximately 26.9 million tons, which is lower than the actual production. The condition MR < MC implies that additional production does not increase marginal profit. Therefore, production optimization strategies should focus on cost efficiency, distribution improvements, and pricing adjustments to achieve the equilibrium condition MR = MC as the optimal production point.