Rework Problem 6.62, except assume that the limit outputs are subject to the following inequality constraints:

\[
\begin{aligned}
& 200 \leq \mathrm{P}_{1} \leq 800 \mathrm{MW} \\
& 100 \leq \mathrm{P}_{2} \leq 400 \mathrm{MW}
\end{aligned}
\]

Problem 6.62

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

\[
\begin{aligned}
& \mathrm{C}_{1}\left(\mathrm{P}_{1}ight)=600+18 \cdot \mathrm{P}_{1}+0.04 \cdot\left(\mathrm{P}_{1}ight)^{2} \\
& \mathrm{C}_{2}\left(\mathrm{P}_{2}ight)=700+20 \cdot \mathrm{P}_{2}+0.03 \cdot\left(\mathrm{P}_{2}ight)^{2}
\end{aligned}
\]

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