## 4 The Implementation of Trends and Results  
The company under analysis is involved in the production and sale of low-voltage plastic cable distribution cabinets, with a focus on the electrical engineering sector. The company's primary activities are centered on the manufacturing, assembly, and delivery of cable distribution boxes. Additionally, the company provides technological equipment and protective components that are part of the main products. Within its strategic group, the company operates in a competitive environment, where both domestic and international competitors are present. The market demands substitute products with similar functions but varying types of materials and designs. The objective of this analysis is to examine the sales of three specific products: product A--fuse boxes, product B--power distribution cabinets, and product C--enclosed terminal blocks over the period of 2020-2024. The dataset utilized in this study comprises sales data for three products, observed over a five-year period from 2020 to 2024. The focus is on evaluating initial sales performance and identifying existing trends. Based on the observed sales dynamics, it is essential to formulate and implement an appropriate strategic approach tailored to each product's market trajectory. Product sales are analyzed through mathematical trends and the Gompertz curve. It is necessary to determine the appropriateness of the relevant trends. Specifying an adequate trend will contribute to the selection of an appropriate product sales strategy. The first trend applied is a linear trend. From Figure 4, it can be seen that a linear trend is not suitable for the sales of product A. The identified trend is described by the equation:  
\[Tr_{t}\ =\ 31.2401+0.3950\cdot x_{t} \tag{20}\]  
Subsequently, a nonlinear trend is applied, which is shown in Figure 5.  
The figure presents the application of a nonlinear trend to the sales of product A. The specified nonlinear trend inappropriately describes the sales of product A. The specific trend is expressed by the equation:  
\[Tr_{t}\ =\ 23.3101+1.1624\cdot x_{t}-0.0126\cdot x_{t}^{2} \tag{21}\]  
It follows from Figure 4 that a linear and a nonlinear trend are not suitable. Prediction interval 95% for product A for linear trend (18.811; 67.351). Prediction interval 95% for product A for nonlinear trend (8.001; 57.060). Figure 4: Linear sales trend for product A. For the specified time series, an exponential trend, specifically the Gompertz curve, was implemented. Sales of Product A show a slow start followed by a steady sales increase. There are visible deviations in certain periods that may reflect fluctuations in demand for product A. An outlier is observed in October 2021 with a sales quantity of 5074 units, which is just below the upper bound of the prediction interval. Over time, sales continued to fluctuate within the predicted interval. Figure 6 illustrates the time series, which shows both increases and decreases in the number of products sold. The dashed lines illustrate the 95% prediction intervals. These intervals are notably wide, reflecting the inherent variability in the dataset and the confidence level of the predictions made by the models. The prediction interval is 95% for product A for Gompertz trend (38.609; 53.892). The exponential trend presented by the Gompertz curve:  
\[T_{t}\ =\ 51.3191\cdot 0.4584^{0.9389^{t}} \tag{22}\]  
The linear and quadratic models used in the analysis are observed to yield almost identical functions, as evidenced by the parameter a\({}_{2}\) in the quadratic trend approaching zero, thereby rendering it effectively linear. To facilitate a clear comparison between models, we present the statistical significance and estimated coefficients for the linear, quadratic, and Gompertz models, as shown in Equations (21)-(23). The statistical significance (\(p\)-value) has been determined for the models presented.