The fuel-cost curves for a two generators power system are given as follows: [begin{aligned}& C_{1}left(P_{1} ight)=600+15 cdot

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

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

While the system losses can be approximated as

\[\mathrm{P}_{\mathrm{L}}=2 \times 10^{-4}\left(\mathrm{P}_{1}\right)^{2}+3 \times10^{-4}\left(\mathrm{P}_{2}\right)^{2}-4 \times 10^{-4} \mathrm{P}_{1} \mathrm{P}_{2}\mathrm{MW}\]

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.