## 3 Materials and Methods
### Description of the System
This is followed by the determination of the constraints used to evaluate the design factors during the experiment. * Experimental tests: Here, the necessary experiments are performed employing an already prepared experimental plan and the response variable data are collected according to the various fusion of the design factor levels. These tests are arbitrarily conducted to reduce the influence of unimportant design factors. * Fitting the Regression models: The regression models are fitted employing the data obtained from the experiments using methods such as the least squares or the maximum likelihood estimation. The resulting regression models are evaluated for their goodness-of-fit to inspect for any discrepancies from the initial model presumptions. * Validation of the regression model: After the model is successfully fitted, it is validated through prediction using further experimental test with unused data. Based on the system described in Section 3.1, the response surface methodology was utilized to develop regression models capable of predicting its net power, CO2 emission and exergy efficiency. The decision variables and their maximum/minimum values, as well as the equations, are shown in Tables 2 and 3 and Equations (10)-(12) respectively [5]. This study considers three objective functions namely:  
1. Net Power Output: The net power, which is a function of the energy analysis, is the summation of the work outputs from the gas turbine and Kalina cycle. Mathematically, it can be expressed as [5]: \[\dot{\mathrm{P}}_{\mathrm{net}}=\dot{\mathrm{P}}_{\mathrm{net,\ GT}}+\dot{ \mathrm{P}}_{\mathrm{net,\ KC}}\] (1) \[\dot{\mathrm{P}}_{\mathrm{net,\ GT}}=\left(\dot{\mathrm{P}}_{\mathrm{GT}-1}+ \dot{\mathrm{P}}_{\mathrm{GT}-2}+\dot{\mathrm{P}}_{\mathrm{GT}-3}\right)- \left(\dot{\mathrm{P}}_{\mathrm{AC}-1}-\dot{\mathrm{P}}_{\mathrm{AC}-2}\right)\] (2) \[\dot{\mathrm{P}}_{\mathrm{net,\ KC}}=\dot{\mathrm{P}}_{\mathrm{ST}}-\dot{ \mathrm{P}}_{\mathrm{pump}-2}\] (3) \[\dot{\mathrm{P}}_{\mathrm{GT}-1}=\dot{\mathrm{m}}_{\mathrm{p}}(\mathrm{h}_{7}- \mathrm{h}_{8})=\dot{\mathrm{P}}_{\mathrm{AC}-1}\] (4) \[\dot{\mathrm{P}}_{\mathrm{GT}-2}=\dot{\mathrm{m}}_{\mathrm{p}}(\mathrm{h}_{8}- \mathrm{h}_{9})=\dot{\mathrm{P}}_{\mathrm{AC}-2}\] (5) \[\dot{\mathrm{P}}_{\mathrm{GT}-3}=\dot{\mathrm{m}}_{\mathrm{p}}(\mathrm{h}_{9}- \mathrm{h}_{10})\] (6)  
where,  
\(\dot{\mathrm{P}}_{\mathrm{net}}\) = net power output;  
\(\dot{\mathrm{P}}_{\mathrm{net,\ GT}}\), \(\dot{\mathrm{P}}_{\mathrm{net,\ KC}}\) = net power from the gas turbines and the Kalina cycle, respectively;  
\(\dot{\mathrm{P}}_{\mathrm{GT}-1}\), \(\dot{\mathrm{P}}_{\mathrm{GT}-2}\), \(\dot{\mathrm{P}}_{\mathrm{GT}-3}\) = net power from gas turbine 1, 2, and 3, respectively;  
\(\dot{\mathrm{P}}_{\mathrm{AC}-1}\), \(\dot{\mathrm{P}}_{\mathrm{AC}-2}\) = net power to compressor 1 and 2, respectively;  
\(\dot{\mathrm{P}}_{\mathrm{ST}}\), \(\dot{\mathrm{P}}_{\mathrm{pump}-2}\) = net power from steam turbine and pump 2 of the Kalina cycle;  
\(\dot{\mathrm{h}}_{7}\), \(\mathrm{h}_{8}\), \(\mathrm{h}_{9}\), \(\mathrm{h}_{10}\) = specific enthalpies at state 7, 8, 9, and 10, respectively;  
\(\dot{\mathrm{m}}_{\mathrm{p}}\) = mass flow rate of the combustion gases from the combustion chamber. \begin{table}
\begin{tabular}{c c} \hline \hline
**Decision Variable** & **Symbol** \\ \hline Compression ratio & Cr \\ Pinch point temperature difference & Pp \\ Inlet turbine temperature & Gt \\ Inlet combustion chamber temperature & Ct \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Decision variables. \begin{table}
\begin{tabular}{c c} \hline \hline
**Decision Variable** & **Minimum and Maximum Values** \\ \hline Compression ratio & \(10\leq\mathrm{Cr}\leq 15\) \\ Pinch point temperature difference & \(10\leq\mathrm{P}\mathrm{p}\leq 30\) \\ Inlet turbine temperature & \(1420\leq\mathrm{Gt}\leq 1520\) \\ Inlet combustion chamber temperature & \(850\leq\mathrm{Ct}\leq 950\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Decision variables and their values. for the global optimum.