Pemodelan Matematika Penentuan Komposisi Gizi Menu Makan Bergizi Gratis untuk Siswa Sekolah Dasar dengan Metode Simpleks

Abstract

To address the issue of nutritional deficiencies among Indonesian children, the government implemented a Free Nutritious Meals (MBG) program that meets 30% of the Recommended Nutrient Intake (RNI) for one meal with five food combinations determined by the Ministry of Health. Research aims to determine the composition of the five food combinations and produce the minimum cost of MBG by constructing a linear programming mathematical model. The budget rules set by the government, along with the required amount of nutrition, were calculated as constraints in the mathematical model. The model, which minimizes the objective function subject to 11 nutritional constraints and one budget constraint, as well as non-negative sign restrictions, was solved using the Simplex Method. The model solution, obtained through several iterations for each combination, was generated using AtoZmath software. The results show that the cost of each combination meets the budget rules, and the minimum cost is in combination 1. Additionally, to ensure the budget costs in combinations 2-5 comply with the budget rules, fruit is excluded from the composition of these combinations.