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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. $1:4$
  2. $2:3$
  3. $3:2$
  4. $4:1$
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