The fuel-cost curves for a two-generator power system are given as follows:

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

while the system losses can be approximated as

\[
\mathrm{P}_{\mathrm{L}}=2 \times 10^{-4}\left(\mathrm{P}_{1}ight)^{2}+3 \times 10^{-4}\left(\mathrm{P}_{2}ight)^{2}-4 \times 10^{-4} \mathrm{P}_{1} \mathrm{P}_{2} \quad \mathrm{MW}
\]

If the system is operating with a marginal cost \((\lambda)\) of \(\$ 60 / \mathrm{hr}\), determine the output of each unit, the total transmission losses, the total load demand, and the total operating cost.