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The fuel cost functions in rupees/hour for two 600 MW thermal power plants are given by Plant 1: C1 = 350 + 6P1 + 0.004P1² Plant 2: C2 = 450 + aP2 + 0.003P2² 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 (λ) is 8 rupees per MW. 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

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

Correct answer: 250, 300

Solution

Plant 1: dC1/dP1 = 6 + 0.008 P1 = 8 gives P1 = 250 MW. With total demand 550 MW, P2 = 300 MW (consistent with a + 0.006(300) = 8). The optimal dispatch is 250 MW and 300 MW, option (250, 350) being wrong; correct is (250, 300).

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