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The fuel cost functions of two power plants are

Plant $P_1$ : $C_1=0.05Pg_1^2+APg_1+B$

Plant $P_2$ : $C_2=0.10Pg_2^2+3APg_2+2B$

where, $P_{g1}$ and $P_{g2}$ are the generated 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

- $1:4$
- $2:3$
- $3:2$
- $4:1$

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