Penerapan Metode Grafik Untuk Menghitung Keuntungan Maksimum Toko Mebel XYZ

Abstract

The furniture industry encompasses various activities, from raw material processing to the production of finished goods. XYZ Furniture Store faces challenges in determining the optimal production quantities of wooden tables and chairs to maximize profits while managing limited resources such as raw materials and production time. This study aims to analyze and find an optimal solution using the graphical method in Linear Programming (LP). The methodology includes problem identification, data collection on per-unit profit, raw material requirements, and production time per product. A mathematical model is developed with an objective function to maximize profit and constraints reflecting available resource limitations. The graphical method is applied by visualizing constraints in a two-dimensional graph to determine the feasible area and evaluating extreme points to identify the optimal solution. The findings indicate that the optimal production quantities are 16.8 units of tables and 6.6 units of chairs per day, yielding a maximum profit of Rp1,104,000. The graphical method proves to be an effective approach for solving optimization problems involving two decision variables—table and chair production—affected by raw material limitations of 30 kg per day and a maximum production time of 40 hours per day. The conclusion of this study provides strategic recommendations for XYZ Furniture Store to enhance production efficiency and profitability. These findings also highlight that Linear Programming is a valuable analytical tool for making production decisions in the furniture industry with constrained resources.