Given two generating units with their respective variable operating costs as:

\[\begin{array}{lll}\mathrm{C}_{1}=0.01 \mathrm{P}_{\mathrm{G} 1}^{2}+2\mathrm{P}_{\mathrm{G} 1}+100 \quad \$ / \mathrm{hr} & \text { for } 25 \leq\mathrm{P}_{\mathrm{G} 1} \leq 150 \mathrm{MW} \\\mathrm{C}_{2}=0.004\mathrm{P}_{\mathrm{G} 2}^{2}+2.6 \mathrm{P}_{\mathrm{G}2}+80 \quad \$ / \mathrm{hr} & \text { for } 30 \leq\mathrm{P}_{\mathrm{G} 2} \leq 200 \mathrm{MW}\end{array}\]

Determine the economically optimum division of generation for \(55 \leq \mathrm{P}_{\mathrm{L}} \leq 350 \mathrm{MW}\). In particular, for \(\mathrm{P}_{\mathrm{L}}=282 \mathrm{MW}\), compute \(\mathrm{P}_{\mathrm{G} 1}\) and \(\mathrm{P}_{\mathrm{G} 2}\). Neglect transmission losses.