Analisis Dualitas Program Linier dalam Optimasi Biaya Produksi Minuman pada Warung Kopi

Abstract

Problems in beverage production in small businesses often occur due to limited raw materials, production time, and operational costs, so that an optimal production combination is needed to minimize costs. This study discusses the application of linear programming duality in optimizing beverage production costs at the "Pak Budi" Coffee Shop with two decision variables, namely the production of Milk Coffee and Iced Coffee. The method used is a linear program with a duality approach and the simplex method to solve the optimization model. The primal minimization model is formed based on the constraints of the availability of coffee beans, milk, ice cubes, sugar, and production time, then transformed into a dual maximization model and solved using the simplex method. The results of the analysis show that the optimal solution is obtained at the production of approximately 2.67 glasses of Milk Coffee and 2 glasses of Iced Coffee with a minimum production cost of Rp21,333.33 per day. In addition, the optimal value of the dual model is the same as the optimal value of the primal model, thus proving the validity of the Strong Duality Theorem. The application of duality and the simplex method has proven effective in determining efficient production combinations and minimizing production costs in small-scale businesses.