## 4 Results
### Model Verification from Sensitivity Analysis  
The sensitivity analysis is divided into sensitivity analysis on variable cells and sensitivity analysis on constraints; the results presented were collected from the report issued by Solver in the resolution of the aggregate planning. The first scenario, with a constant workforce and new power demand, shows that the reduced cost of the variables is either positive or equal to zero; that is, the variables are part of the solution, and there is no slack. The exception is the dismissed workers variable, which has a negative reduced cost; it shows that it has extra workers for production due to the cooperative's capacity. As for the permission to increase or reduce, without modifying the optimal solution, the only variable that allows an increase in its cost is that of the workforce, presenting a different increase in each period, and the variables that enable the reduction are the production of hours overtime, production, and laid-off workers. The one for dismissed workers allows a different value for each period, while the others present the same value for all. Variables with a value equal to zero cannot be changed because the optimal solution is also changed. As for restrictions, contractors, production, and overtime have a favorable shadow price; the objective function will increase when they are increased. For example, if the number of overtime hours increases, the cost of the objective function will also increase. The workforce, in turn, has a negative shadow price; if the workforce increases, the optimal \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Period** **(Month)**} & **Contractors** **(Number of People)** & **Fired (Number of People)** & **Workforce (Number of People)** & **Production in Overtime (Hours)** & **Production (kg)** & **Power Demand (kW)** & **Production Demand (kg)** \\ \hline
0 & 0 & 0 & 17 & 0 & 0 & 235 & 0 \\ \hline
1 & 0 & 2 & 15 & 0 & 73,058.02 & 235 & 73,058.02 \\ \hline
2 & 0 & 0 & 15 & 0 & 48,155.40 & 235 & 48,155.40 \\ \hline
3 & 0 & 0 & 15 & 0 & 80,745.51 & 235 & 80,745.51 \\ \hline
4 & 0 & 0 & 15 & 0 & 70,974.94 & 235 & 70,974.94 \\ \hline
5 & 0 & 0 & 15 & 0 & 73,072.40 & 235 & 73,072.40 \\ \hline
6 & 0 & 0 & 15 & 0 & 75,037.28 & 235 & 75,037.28 \\ \hline
7 & 0 & 0 & 15 & 1 & 78,020.75 & 235 & 78,020.75 \\ \hline
8 & 0 & 0 & 15 & 28 & 92,827.75 & 235 & 92,827.75 \\ \hline
9 & 0 & 0 & 15 & 4 & 80,068.89 & 235 & 80,068.89 \\ \hline
10 & 0 & 0 & 15 & 0 & 69,798.75 & 235 & 69,798.75 \\ \hline
11 & 0 & 0 & 15 & 7 & 81,646.55 & 235 & 81,646.55 \\ \hline
12 & 0 & 0 & 15 & 11 & 83,557.78 & 235 & 83,557.78 \\ \hline Total cost & & & & 14,284,113.02 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Aggregate plan as a proposed scenario considering power demand. solution is not changed since the Solver interprets the surplus of workers due to production capacity. This is because 17 workers have been fixed as a restriction of the cooperative. As for the permission to increase, it is possible to increase the cost of the workforce by up to R5 0.85 in all periods, those hired by up to R5 0.93 in the first eight periods, overtime by 671.22 h in the eighth period, and in all others in 680 h, the maximum limit that can be accomplished. The production constraint has a different increase limit for each period. As for the permission to reduce, the restriction of contractors does not allow reduction due to the limit set by the cooperative. The workforce can be reduced by 0.93 kg in the first eight periods, while it cannot be reduced in the others. Production can only be reduced in the eighth period by 4827.76 kg. In the second scenario, allowing hiring and firing with the new power demand in the variables, the reduced cost remains the same as in the previous scenario. It can be noted that the dismissed workers, in this scenario, have zero cost, different from the last scenario, because now the restriction allowed to keep at least 15 workers, no more than necessary.