The fuel cost functions in rupees/hour for two 600 MW thermal power plants are given by

Plant 1 : C₁ = 350 + 6P₁ + 0.004P$$_1^2$$

Plant 2 : C₂ = 450 + aP₂ + 0.003P$$_2^2$$

where P₁ and P₂ are power generated by plant 1 and plant 2, respectively, in MW and a is constant. The incremental cost of power ($$\lambda$$) is 8 rupees per MWh. The two thermal power plants together meet a total power demand of 550 MW. The optimal generation of plant 1 and plant 2 in MW, respectively, are

Consider the economic dispatch problem for a power plant having two generating units. The fuel costs in $$Rs/MWh$$ along with the generation limits for the two units are given below:
$$\eqalign{ & {C_1}\left( {{P_1}} \right) = 0.01\,P_1^2 + 30{P_1} + 10; \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,100\,MW \le {P_1} \le 150\,MW \cr} $$
$$\eqalign{ & {C_2}\left( {{P_2}} \right) = 0.05\,P_2^2 + 10{P_2} + 10; \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,100\,MW \le {P_2} \le 180\,MW \cr} $$

The incremental cost (in $$Rs/MWh$$) of the power plant when it supplies $$200$$ $$MW$$ is __________.

The incremental costs (in rupees/$$MWh$$) of operating two generating units are functions of their respective powers $${P_1}$$ and $${P_2}$$ in $$MW,$$ and are given by $$${{d{C_1}} \over {d{P_1}}} = 0.2{P_1} + 50$$$ $$${{d{C_2}} \over {d{P_2}}} = 0.24{P_2} + 40$$$
Where, $$$\eqalign{ & 20\,MW \le {P_1} \le 150\,MW \cr & 20\,MW \le {P_2} \le 150MW. \cr} $$$
For a certain load demand, $${P_1}$$ and $${P_2}$$ have been chosen such that $$\,\,d{C_1}/d{P_1} = 76\,Rs/MWh\,\,$$ and $$\,d{C_2}/d{P_2} = 68.8\,Rs/MWh.\,\,$$ If the generations are rescheduled to minimize the total cost, then $${P_2}$$ is ____________.

The fuel cost functions of two power plants are
Plant $${P_1}:\,{C_1} = 0.05\,Pg_1^2 + AP{g_1} + B$$
Plant $${P_2}:\,{C_2} = 0.10\,Pg_2^2 + 3AP{g_2} + 2B$$
Where, $$P{g_1}$$ and $$P{g_2}$$ are the generator powers of two plants and $$A$$ and $$B$$ are the constants. If the two plants optimally share $$1000$$ $$MW$$ load at incremental fuel cost of $$100$$ $$Rs/MWh,$$ the ratio of load shared by plants $${P_1}$$ and $${P_2}$$ is