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The fuel cost functions in rupees/hour for two $600$ $\text{MW}$ thermal power plants are given by

Plant $1$ : $C_{1} = 350 + 6P_{1} + 0.004P_{1}^{2}$

Plant $2$ : $C_{2} = 450 + aP_{2} + 0.003P_{2}^{2}$

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

  1. $200, 350$
  2. $250, 300$
  3. $325, 225$
  4. $350, 200$
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