GATE Electrical Engineering (EE) 2015 Shift 2 Solved Paper

The incremental costs (in rupees/MWh) of operating two generating units are functions of their respective powers ${\mathrm{P}}_1$ and ${\mathrm{P}}_2$ in $\mathrm{MW}$, and are given by
$\frac{{\mathrm{dC}}_1}{{\mathrm{dP}}_1}=0.2{\mathrm{P}}_1+50$
$\frac{{\mathrm{dC}}_2}{{\mathrm{dP}}_2}=0.24{\mathrm{P}}_2+40$
Where,
$20\mathrm{MW}\le {\mathrm{P}}_1\le 150\mathrm{MW}$
$20\mathrm{MW}\le {\mathrm{P}}_2\le 150\mathrm{MW}$
For a certain load demand, $\mathrm{P}1$ and $\mathrm{P}2$ have been chosen such that $\mathrm{dC}1∕\mathrm{dP}1=76\mathrm{Rs}∕\mathrm{MWh}$ and $\mathrm{dC}2∕\mathrm{dP}2=68.8\mathrm{Rs}∕\mathrm{MWh}$. If the generations are rescheduled to minimize the total cost, then $\mathrm{P}2$ is___