Rework problem 12.19 except assume that the limit outputs are subject to the following inequality constraints:

\[\begin{aligned}& 200 \leq \mathrm{P}_{1} \leq 800 \mathrm{MW} \\& 100 \leq\mathrm{P}_{2} \leq 500 \mathrm{MW}\end{aligned}\]

Data From Problem 12.19:-

The fuel-cost curves for two generators are given as follows:

\[\begin{aligned}& \mathrm{C}_{1}\left(\mathrm{P}_{1}\right)=600+15 \cdot\mathrm{P}_{1}+0.05 \cdot\left(\mathrm{P}_{1}\right)^{2} \\&\mathrm{C}_{2}\left(\mathrm{P}_{2}\right)=700+20 \cdot \mathrm{P}_{2}+0.04\cdot\left(\mathrm{P}_{2}\right)^{2}\end{aligned}\]

Assuming the system is lossless, calculate the optimal dispatch values of \(\mathrm{P}_{1}\) and \(\mathrm{P}_{2}\) for a total load of \(1000 \mathrm{MW}\), the incremental operating cost, and the total operating cost.