n electrical system is divided into four areas managed by electrical companies that are independent of each other. The expected consumption for a given hour and the generation cost curves of each company are as follows:

Determine : a. The generation costs of each company if there are no energy exchanges between them. b. Generation costs and power exchanges if the four companies decide to coordinate their generations in economic dispatch.

\begin{tabular}{cccc} Compay & Costs/h & LmitMW & DemandMW \\ \hline 1 & 350+4P+0.002P2 & 1000P2000 & 1500 \\ 2 & 425+5P+0.005P2 & 500P1000 & 700 \\ 3 & 375+10P+0.002P2 & 500P1000 & 800 \\ 4 & 500+12.5P+0.0075P2 & 100P500 & 400 \\ \hline \end{tabular}