Given an AGC area with two generators. The operating costs for the two generators are

$C_1=2,000+50P_{r,1}$

$C_2=1,000+0\mathrm{.}2P_{r,2}^2$

where $P_{r,i}$ is the reference power for generator $i$ in MW$.$ What are $P_{r,1}$ and $P_{r,2}$ and $C_T($total operating cost$)$ for the area's total $P_{\text{r}\text{e}\text{f}}=400,500,$ and $600$ MW $?$

$2.$ Repeat $(1)$ above with

$C_1=2,000+50P_{r,1}+0\mathrm{.}1P_{r,1}^2$

$C_2=1,000+0\mathrm{.}2P_{r,2}^2$