Diet Package Profit Optimization of a Fitness Center Using the Simplex Method and POM-QM Software

Abstract

The growing trend of healthy lifestyles has encouraged fitness centers to provide supporting services in the form of healthy meal packages tailored to customers’ nutritional needs. This study aims to optimize the profit of diet package production at a fitness center using the simplex method and POM-QM software. The research employed a descriptive quantitative approach using secondary data consisting of profit per package, resource requirements, and available resource capacities. The study focused on two types of diet packages, namely the High-Protein Package and the Balanced Package, with limited resources of 500 kg of food ingredients, 2,000 hours of nutritionist consultation time, and 1,500 hours of kitchen capacity per month. The mathematical model was formulated into an objective function and constraint functions, then solved manually using the simplex method and validated using POM-QM for Windows software. The results showed that the optimal solution was achieved by producing 100 High-Protein Packages and no Balanced Packages. This combination generated a maximum profit of Rp25,000,000 per month. Both manual calculations and POM-QM software produced the same results, indicating that the simplex method is capable of providing accurate optimal solutions. In addition, the use of POM-QM software accelerated the analysis process, minimized calculation errors, and facilitated the visualization of optimization results. Therefore, the simplex method and POM-QM software are effective tools for decision-making in determining the optimal production strategy for diet packages at fitness centers.