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Two generators have cost functions $F_{1}$ and $F_{2}$ . Their incremental-cost characteristics are

  • $\dfrac{dF_{1}}{dP_{1}}=40+0.2P_{1}$
  • $\dfrac{dF_{2}}{dP_{2}}=32+0.4P_{2}$

They need to deliver a combined load of $260$ $\text{MW}$. Ignoring the network losses, for economic operation, the generations $P_{1}$ and $P_{2}$ (in $\text{MW}$) are

  1. $P_{1}=P_{2}=130$
  2. $P_{1}=160, P_{2}=100$
  3. $P_{1}=140, P_{2}=120$
  4. $P_{1}=120, P_{2}=140$
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