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  1. The incremental costs (in Rupees/M Wh) of operating two generating units are functions of their respective powers P1 and P2 in MW, and are given by
    dC1
    = 0.2P1 + 50;
    dC2
    = 0.24P2 + 40;
    dP1dP2

    Where
    20 MW ≤ P1 ≤ 150 MW
    20 MW ≤ P2 ≤ 150 MW
    For a certain load demand, P1 and P2 have been chosen such that dC1 /dP1 = 76 Rs/MWh and dC2/dP2 = 68.8 Rs/MWh. If the generations are rescheduled to minimize the total cost, then P2 is __________.
    1. 130
    2. 1360
    3. 1.036
    4. 136.36
Correct Option: D

=
dc1
= 76 = 0.2P1 + 50
dP1

⇒ P1 = 130
and
dc2
= 68.8 = 0.24P2 + 40
dP2

∴ P2 = 120
∴ P1 + P2 = 130 + 120 = 250
For minimization of total cost
dc1
=
dc2
dp1dp2

∴ 0.2p1 + 50 = 0.24p2 + 40
∴ 0.2[250 – P2] + 50 = 0.24P2 + 40
∴ P2 = 136.36



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