## 3 The Case Study
#### Mathematical Modeling--Relations
The approximate weight of a regular semi-cylindrical PET bottle is around 10 g. If a successful bottle redesign achieves an 8% weight reduction, the weight of the fully cylindrical PET bottle would be approximately 9.2 g. Around 1.6 billion plastic bottles are produced daily worldwide, while annual PET bottle production is estimated at 583.3 billion units [90]. This volume of production corresponds to approximately 54,800 metric tons of PET daily, or around 20 million tons annually [91]. An 8% reduction in material usage would translate to approximately 4384 tons less material usage per day, or about 1,600,000 tons annually, for the production of the same number of volume-identical bottles. Figure 5 illustrates this material reduction, showing a decrease in annual material consumption from 20 million to 18.4 million tons as a result of the packaging redesign. In economic terms, this reduction in material usage leads to enormous cost savings. According to Plastics Information Europe [92], the price of PET in May 2022 was approximately 1887 U.S. dollars or 1760 euros per metric ton. As shown above, reducing annual PET usage by 1,600,000 tons corresponds to a cost reduction of 3,019,200,000 U.S. dollars or 2,816,000,000 euros. In an ever-changing world, and with the emergence of environmental problems caused by industrial production, reducing the use of materials and energy--wherever possible--is imperative. The use of plastic has increased over the years, partly due to its contribution to the protection and preservation of food [61]. According to Ellen MacArthur Foundation et al. [93], beyond its physical characteristics--such as low weight, which contributes to reduced transport costs and various environmental benefits--it is also a low-cost material that offers high levels of protection to the contained product. This enhanced protection further contributes to a reduced environmental impact by preserving energy resources and raw materials [94]. The above analysis underlines the combined environmental and economic benefits that may result from effective packaging redesign. Today, when even the slightest change in industrial production can affect the environment to varying degrees, interventions such as packaging redesign--which may lead to a significant reduction in material usage and further environmental mitigation--are essential (Figure 6). Figure 5: Material volume reduction based on packaging redesign. The concept of packaging redesign in terms of material reduction (without compromising product protection) is of high importance and should be considered a critical issue for both industry and governments. While efforts to protect the environment have become more intense in recent years, governments increasingly focus on imposing taxes through concepts such as the Polluter Pays Principle [95] (The principle is based on the concept that the polluters bear the costs of their pollution. These costs include the costs of measures adopted to prevent, properly manage, and protect the environment from the burden caused by the polluter.). In addition to this principle, and based on the findings of the present investigation, governments should consider providing incentives to producers to reduce their environmental impact by pursuing a partial or total redesign of their product packaging, instead of imposing taxes that are ultimately passed on to final consumers through higher product prices. Incentives for industries that succeed in becoming involved may include economic reliefs and could be evaluated by connecting measurable data on the basis of reducing the product's environmental footprint as a result of the packaging redesign as well as the reduction in material and energy usage. On the other hand, the economic benefits for the organizations are equally significant. As we saw above, the significant economic savings in material usage as a result of a sophisticated packaging redesign should be taken into consideration by the managers.