Analysis of Production Cost Efficiency of Coffee Shop Business "Prestasi Kopi" at Medan State University Based on Linear Equation System and Inverse Matrix in Marginal Cost Analysis, Marginal Revenue, and BEP - Yudhistira Sadewa; Loranty Folia Simanjuntak; Yohanes Afrinkus; Bela Magdalena; Luna Selciella; Shella Halim (Outline Journal of Economic Studies, 2026)
Purpose: This study aimed to analyze the efficiency of production costs in the "Prestasi Kopi" coffee shop located at Universitas Negeri Medan using a mathematical approach based on a system of linear equations and inverse matrices. Methods: The research employed a descriptive-quantitative method through direct observation and in- depth interviews with the business owner and managers. The collected data included the structure of fixed costs, variable costs, and sales data of coffee products, specifically the Sea Salt Butterscotch, Choco Hazelnut, and Sanger Prestasi Kopi. The analysis utilized a system of linear equations and the inverse matrix method to model the components of production costs, obtaining the total cost and total revenue functions as the basis for calculating the marginal cost, marginal revenue, and break-even point in units and rupiah. Results: The findings showed that the "Prestasi Kopi" coffee shop exceeded the break-even point with a marginal revenue value greater than the marginal cost. Conclusions: This indicated a profitable business condition and an efficient cost structure, proving that this mathematical approach was effective in supporting managerial decision-making for small businesses in a university environment. Originality/value: This study provided empirical evidence on the practical application of mathematical economics to evaluate andoptimize the financial performance of micro-enterprises.