## 3 Results and Discussion
### Rotatable Central Composite Design  
This experiment considered the previously obtained results, which indicated that higher pH values and temperatures could minimize the production of 1,3-propanediol. The variables of this experiment were chosen from the most promising variables in the 2\({}^{3}\) factorial design. Figure 8 shows how lactic acid and 1,3-propanediol were obtained in the experiments using an M9 medium supplemented with 4% glycerol. It was possible to verify that, with the experiments' design, there was a higher production of lactic acid and a reduced production of 1,3-propanediol. The significance of the effects of inoculum concentration and pH were evaluated for the experiments presented in Table 3 using glycerol as a carbon source, based on analysis of variance (ANOVA) using the TIBCO Statistica program as a tool. The Pareto diagram for standardized effects concerning lactic acid production (Figure 9A) indicates that inoculum concentration and pH are significant for lactic acid production and satisfy the evaluated range's statistical hypothesis. The ANOVA test showed that the inoculum concentration effect was significant for lactic acid production. The effect of the quadratic ratio of pH and inoculum concentration was also significant, as was the effect of the ratio of inoculum concentration to pH. The confidence level for these analyzes was 95% (\(p\) = 0.05). Figure 9B represents the model's ability to predict glycerol consumption, indicating that the regression model satisfactorily predicts the experimental data. The regression model for experiment assays using glycerol as a carbon source with a correlation coefficient (R\({}^{2}\)) of 92.08% can be expressed as:  
\[\mathrm{Y}=45.07-3.33\cdot\mathrm{X}_{1}^{2}-4.48\cdot\mathrm{X}_{2}^{2} \tag{5}\]  
The results corroborate those obtained in the Pareto diagram, indicating that higher inoculum concentrations tend to produce more lactic acid. When analyzing the pH factor, there is a greater tendency towards production near the central point, indicating that the medium must have a pH of 9.5. [PERSON] et al. (2018) observed that, at a pH from 7.1 to 8.0, the dominant byproduct was lactic acid in fed-batch fermentation by _K. pneumoniae_. Figure 8: Production of lactic acid and 1,3-propanediol obtained in M9 medium with 4% glycerol for 72 h was related to the rotational composite central design experiments. With the surface graph and contour plot shown in Figure 10A,B, it is possible to verify the point of maximum glycerol consumption. This fact shows that higher glycerol consumption conditions are the central point, and are also the best conditions for the production of lactic acid. Fermentation was carried out for 72 h, reaching the theoretical point of the maximum consumption of glycerol, making longer fermentations unnecessary. It was possible to find the point of the maximum consumption of glycerol, maximize the production of lactic acid and significantly reduce the production of 1,3-propanediol with the experimental design. Compared to the 2\({}^{3}\) factorial design experiment, lactic acid production remained close to 3 g\(\cdot\)L\({}^{-1}\), and the production of 1,3-propanediol dropped to 0.8 g\(\cdot\)L\({}^{-1}\), showing an evident improvement that was only achieved by modifying simple  
Figure 9: (**A**) Pareto chart for standardized effect estimative of the inoculum concentration (X\({}_{1}\)) and pH (X\({}_{2}\)) and (**B**) prediction of the regression model for experimental data for the glycerol consumption (N.B. linear fit: \(y=3.1195+0.9208\cdot x\)). The dashed lines stand for the regression bands built with a 95% confidence level. process variables. It is worth mentioning that it was possible to induce bacteria to produce lactic acid, a non-preferred route. In this experiment, the yield was Y\({}_{\text{LA/Gly}}\) 0.68, higher than the 2\({}^{3}\) factorial design. For 1,3-propanediol, the lowest yield value was achieved among the experiments: Y\({}_{\text{1,3-PDO/Gly}}\) 0.18. [PERSON] et al.