## 4 Results and Discussion
### Optimal Investment Allocation  
The stochastic model outlines a strategic allocation of investments among three renewable energy projects--Solar Farm, Wind Farm, and Hydro Plant--over five years. Table 10 delineates the appropriate investment allocations and associated capacity expansions for each project during the specified periods. Figure 3 depicts the ideal investment allocation per project per year as determined by stochastic optimization. The capacity expansion per project per year is shown in Figure 4. Similarly, Figure 5 describes the Operational Decisions Heatmap.  
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Year** & **Project** & **Investment (USD)** &
\begin{tabular}{} **Capacity** \\ **Expansion (MW)** \\ \end{tabular} \\ \hline
1 & Solar & 2,500,000.00 & 80.00 MW \\ \hline  & Wind & 2,500,000.00 & 65.00 MW \\ \hline  & Hydro & 0.00 & 40.00 MW \\ \hline
2 & Solar & 2,000,000.00 & 80.00 MW \\ \hline  & Wind & 2,000,000.00 & 65.00 MW \\ \hline  & Hydro & 0.00 & 40.00 MW \\ \hline
3 & Solar & 1,500,000.00 & 80.00 MW \\ \hline  & Wind & 1,500,000.00 & 65.00 MW \\ \hline  & Hydro & 0.00 & 40.00 MW \\ \hline
4 & Solar & 1,250,000.00 & 80.00 MW \\ \hline  & Wind & 1,250,000.00 & 65.00 MW \\ \hline  & Hydro & 0.00 & 40.00 MW \\ \hline
5 & Solar & 1,000,000.00 & 80.00 MW \\ \hline  & Wind & 1,000,000.00 & 65.00 MW \\ \hline  & Hydro & 0.00 & 40.00 MW \\ \hline \hline \end{tabular}
\end{table}
Table 10: Optimal Investment Allocation and Capacity Expansion.  
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt}} \hline \hline
**Parameter** & **Value** \\ \hline  & Nonzeros: 362 \\ Presolve Reduction & Rows Removed: 154 \\ \hline  & Columns Removed: 75 \\ \hline  & Nonzeros Remaining: 88 \\ \hline Model Size (Post-Presolve) & Rows: 10 \\ \hline  & Columns: 20 \\ \hline  & Nonzeros: 88 \\ \hline Optimal Iterations & 6 \\ \hline Total Optimization Time & 0.12 s \\ \hline Work Units & 0.00 \\ \hline Optimal Objective Value & \$1,772,500 \\ \hline Presolve Time & 0.04 s \\ \hline \end{tabular}
\end{table}
Table 9: _Cont._Figure 4: Capacity Expansion per Project per Year.  
Figure 3: Investment Allocation per Project per Year.  
Table 9 shows the investment breakdown and capacity increases of renewable energy projects under a stochastic optimization framework. Solar and wind consistently receive funding throughout the five-year period, which helps them expand their capacities entirely by the end of the period and maintain operations thereafter. On the other hand, Hydro does not receive investments but sees a partial capacity increase of 40 MW each year. The investment strategy in the stochastic model prioritizes solar and wind projects by allocating capital during the year of operation for both projects. Solar, reaching 80 MW, and wind, reaching 65 MW, show a strong dedication to improving these energy sources. The projected return rates indicate returns and favourable risk profiles for wind projects (Solar is projected to yield 12% under Stable and High Price conditions in Year 1), influencing the decision-making process. Although not receiving investments like solar and wind projects, Hydro steadily increases its capacity by 40 MW annually. This approach shows a decision to sustain Hydro capabilities without requiring more financial resources, either because of its cost-effectiveness or reliability as a hydroelectric business entity. The lack of funding allocated to Hydro might stem from constraints in the budget or the expected returns compared to solar and wind energy projects. The gradual decrease in investment, starting from USD 2.5 million in Year 1 to USD 1 million in Year 4, aligns with the decreasing budgets over the five years (USD 5 million in Year 1 down to USD 2 million in Year 5). This plan of action ensures that the first few years receive funding to support growth opportunities, and the focus shifts in the later years towards maintaining and improving existing capacities within financial limitations.