A power system has two generators with the following cost curves
Generator $$1:$$ $${C_1}\left( {{P_{G1}}} \right) = 0.006\,P_{G1}^2 + 8{P_{G1}} + 350$$ (Thousand Rupees/Hour)
Generator $$2:$$ $${C_2}\left( {{P_{G2}}} \right) = 0.006\,P_{G2}^2 + 7{P_{G2}} + 400$$ (Thousand Rupees/Hour)
The generator limits are
$$\eqalign{ & 100\,MW \le {P_{G1}} \le 650\,MW \cr & 50\,MW \le {P_{G2}} \le 500\,MW \cr} $$

A load demand of $$600$$ $$MW$$ is supplied by the generators in an optimal manner. Neglecting losses in the transmission network, determine the optimal generation of each generator.

In a power system, the fuel inputs per hour of plants $$1$$ and $$2$$ are given as
$${F_1} = 0.20\,P_1^2 + 30\,{P_1} + 100\,\,$$ Rs per hour
$${F_2} = 0.25\,P_2^2 + 40\,{P_2} + 150\,\,$$

The limits of generators are $$$\eqalign{ & 20 \le {P_1} \le 80\,MW \cr & 40 \le {P_2} \le 200\,MW \cr} $$$
Find the economic operating schedule of generation, If the load demand is $$130$$ $$MW.$$ neglecting transmission losses.