Optimized Design of Laundry Cleaning Based on Linear Programming
Tiantian Huang
DOI: https://doi.org/10.59429/esta.v10i6.1672
Keywords: Laundry Cleaning Optimization Design; Linear Programming
Abstract
This paper presents an optimized design for laundry cleaning, utilizing linear programming and Python and SPSS software programming. It aims to achieve cost-effective and good cleaning effects under different conditions. The core challenge addressed in this paper is balancing cost-effectiveness and cleaning effectiveness. First, a mathematical model is developed to describe dirt solubilization in water and the relationship between wash frequency and water consumption. Second, a cost-effective cleaning scheme is identified, considering water rates and other factors. Additionally, factors such as clothing types and quantities, dirt types, detergent types, and the constraint of mixing certain clothing items during washing are taken into account. By solving the laundry cleaning mathematical problems using an optimization model in mathematical modeling, factor analysis is conducted considering various factors including a given amount of dirt, water, dirt solubility in water (function), wash frequency, water consumption per wash, dirt type, detergent type, detergent solubility in dirt, detergent unit price, water rates, and the constraint of certain clothing items not being able to be washed together. The goal is to achieve a lower-cost laundry cleaning solution that is both effective and tidy.
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