The expressions of fuel cost of two thermal generating units as a function of the respective power generation $P_{G 1}$ and $P_{G 2}$ are given as
$F_{1}\left(P_{G 1}\right)=0.1 a P_{G 1}^{2}+40 P_{G 1}+120 ~\mathrm{Rs} / \text { hour } \qquad 0 \text{MW} \leq P_{G 1} \leq 350 \text{MW}$
$F_{2}\left(P_{G 2}\right)=0.2 P_{G 2}^{2}+30 P_{G 2}+100 ~\mathrm{Rs} / \text { hour } \qquad 0 \text{MW} \leq P_{G 2} \leq 300 \text{MW}$
where $a$ is a constant. For a given value of $a,$ optimal dispatch requires the total load
of $290 ~\mathrm{MW}$ to be shared as $P_{G 1}=175 ~\mathrm{MW}$ and $P_{G 2}=115 ~\mathrm{MW}.$ With the load remaining unchanged, the value of $a$ is increased by $10 \%$ and optimal dispatch is carried out. The changes in $ P_{G 1}$ and the total cost of generation, $F(= F_{1}+F_{2})$ in $\text { Rs/hour}$ will be as follows
- $P_{G 1}$ will decrease and $F$ will increase
- Both $P_{G 1}$ and $F$ will increase
- $P_{G 1}$ will increase and $F$ will decrease
- Both $P_{G 1}$ and $F$ will decrease