Optimization Of Tofu Production Planning In Small And Medium Enterprises Using Linear Programming With The Simplex Method

Abstract

Mr. Rezeki Tofu SME in Pematangsiantar faces challenges in traditional production planning, which is not optimal for managing demand fluctuations and resource allocation. This study aims to formulate an optimal production plan to maximize daily profit by efficiently allocating resources using Linear Programming with the Simplex method. A descriptive qualitative research approach was employed, gathering primary data through direct observation and secondary data through interviews and documentation. Decision variables included the production quantities of White Tofu, Fried Tofu, and Yellow Tofu, constrained by raw materials (soybeans, vinegar, cooking oil, turmeric) and production time. The continuous optimization results revealed an optimal mix of 12.2947 barrels of White Tofu, 50 barrels of Fried Tofu, and 50 barrels of Yellow Tofu, achieving a maximum profit of IDR 5,745,893.72 per day. For operational implementation, rounding to 12 barrels of White Tofu, 50 barrels of Fried Tofu, and 50 barrels of Yellow Tofu yields a daily profit of IDR 5,740,000.00 (a minor decrease of 0.103%). Slack resource analysis identified soybeans, cooking oil, and turmeric as binding constraints, whereas vinegar and production time remained underutilized. In conclusion, the Simplex method effectively enhances resource allocation efficiency and profitability, indicating that production capacity expansion should prioritize securing scarce raw materials rather than extending working hours.