## 3. Results and Discussion
### Volume-Fixed Optimal Equal Bale Dimensions Design
the optimal bale dimensions are given by Equation (19) and film usage_  
\[FC(p_{b})=\frac{4b_{f}}{(\epsilon_{t/t}+1)\left[\sqrt[3]{\frac{170 _{0}}{\pi}}\right]^{2}}\left\{\left[p_{b}\frac{\sqrt[3]{\frac{170_{0}}{\pi}} \left[\frac{2}{1-\frac{1}{\tilde{\epsilon}}_{B}(p_{b})}-\left(\frac{p_{l}}{p_ {b}}-1\right)\right]}{b_{f}}\right]+\frac{4}{\pi}\left[\frac{\pi\sqrt[3]{\frac {170_{0}}{\pi}}\left(p_{l}-p_{b}\right)}{2b_{f}}\right]\right\}. \tag{46}\]  
_Integer \(p_{b}^{*}\) solving Problem 4 is defined by optimization task expressed by Equation (36)._  
Thus, the inequalities specified in the proposition must be solved for two variables: integer \(p_{b}\) and continuous \(k_{fb}\). Next optimization task, Equation (36), must be solved and the overlap \(\delta\) can be computed. Example 4  
Film parameters and overlap ratio \(k_{f}\) as in the previous examples are given. Film widths \(b_{f}=0.75\), \(0.9\) m, even \(p\) such that \(4\leq p_{l}\leq 16\) and bale volume \(V_{b0}=1.357\) m\({}^{3}\) are assumed. For any \(p_{l}\) the sets of overlap ratios \(k_{fb}\) satisfying inequalities from Equations (41) and (42) are given in the fourth column of Table 5. As previously, for any \(k_{fb}\) from these closed intervals the linear formulas from Equation (45) for computing \(\delta\) are given in the next column, in the last column film consumptions \(FC(p_{b})\), Equation (46), are enclosed. For these \(p_{l}\) for which there are more than one \(p_{b}\) such that inequalities from Equations (41) and (42) are satisfied the minimal film usage, solving optimization task from Equation (36), is marked by bold. Note that in most cases film usage for \(b_{f}=0.9\) m is smaller from that for \(b_{f}=0.75\) m; this confirms the analysis of the film width influence on the optimal film usage from [14,20]--the broader film width is applied, the smaller minimal film usage is achieved. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(\mathbf{b}_{f}\left[\mathbf{m}\right]\) & \(\mathbf{p}_{l}\) & \(\mathbf{p}_{b}\) & \(k_{fb}\left[-\right]\) & \(\delta\)\(\left[\mathbf{m}\right]\) & \(FC\)\(\left[\mathbf{m}^{-1}\right]\) \\ \hline \multirow{8}{*}{0.75} & 4 & 2 & [0.200, 0.311] & 0.886\(\cdot k_{fb}\) & 20.726 \\  & 6 & 3 & [0.200, 0.311] & 0.886\(\cdot k_{fb}\) & 30.309 \\  & 8 & 3 & [0.428, 0.439] & 1.286\(\cdot k_{fb}-0.4\) & **41.232** \\  & 8 & 4 & [0.200, 0.311] & 0.886\(\cdot k_{fb}\) & 41.453 \\  & 10 & 4 & [0.380, 0.412] & 1.186\(\cdot k_{fb}-0.3\) & **50.815** \\  & 10 & 5 & [0.200, 0.311] & 0.886\(\cdot k_{fb}\) & 51.036 \\  & 12 & 5 & [0.346, 0.394] & 1.126\(\cdot k_{fb}-0.240\) & 61.958 \\  & 12 & 6 & [0.200, 0.311] & 0.886\(\cdot k_{fb}\) & **60.619** \\  & 14 & 6 & [0.322, 0.382] & 1.086\(\cdot k_{fb}-0.2\) & 71.541 \\  & 14 & 7 & [0.200, 0.311] & 0.886\(\cdot k_{fb}\) & 71.762 \\  & 14 & 8 & [0.200, 0.204] & 0.736\(\cdot k_{fb}+0.15\) & **70.423** \\  & 16 & 6 & [0.428, 0.439] & 1.286\(\cdot k_{fb}-0.4\) & **80.903** \\  & 16 & 7 & [0.304, 0.372] & 1.057\(\cdot k_{fb}-0.171\) & 81.124 \\  & 16 & 8 & [0.200, 0.311] & 0.886\(\cdot k_{fb}\) & 81.345 \\  & 16 & 9 & [0.200, 0.222] & 0.752\(\cdot k_{fb}+0.133\) & 81.566 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The numbers of global \(p_{l}\) and bottom \(p_{b}\) film layers, bottom layers overlaps \(k_{fb}\), \(\delta\) fulfilling inequalities from Equations (41) and (42), and respective film usage \(FC\), Equation (46), for \(V_{b0}=1.357\) m\({}^{3}\) and bale from Example 4; film widths \(b_{f}=0.75\), \(0.9\) m, the bounds from Equations (22) and (23): \(k_{fb,min}=0.2\), \(k_{fb,max}=0.45\), \(\delta_{min}=0.15\) m, \(\delta_{max}=0.3\) m, \(4\leq p_{l}\leq 16\). Minimal film usage solving Problem 4 of volume-fixed design of equal optimal bale dimensions is marked by bold.