Chapter 6, Problem 6.62P

The fuel-cost curves for two generators are given as follows: $\begin{array}{l}{C}_1\left(P{1}_{}\right)=600+18\cdot P_1+0.04\cdot {\left(P_1\right)}^2\\ C_2\left(P_2\right)=700+20\cdot P_2+0.03\cdot {\left(P_2\right)}^2\end{array}$

Assuming the system is lossless, calculate the optimal dispatch values of $P_1$ and $P_2$ for a total load of 1000 MW, the incremental operating cost, and the total operating cost.