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\hline Q.21 & $\begin{array}{l}\text { The expressions of fuel cost of two thermal generating units as a function of the } \\ \text { respective power generation } P_{G 1} \text { and } P_{G 2} \text { are given as } \\ F_{1}\left(P_{G 1}\right)=0.1 a P_{G 1}^{2}+40 P_{G 1}+120 \mathrm{Rs} / \text { hour } \\ F_{2}\left(P_{G 2}\right)=0.2 P_{G 2}^{2}+30 P_{G 2}+100 \mathrm{Rs} / \text { hour } \\ \text { where } a \text { is a constant. For a given value of } a, \text { optimal dispatch requires the total load } \\ \text { of } 290 \mathrm{MW} \text { to be shared as } P_{G 1}=175 \mathrm{MW} \text { and } P_{G 2}=115 \mathrm{MW} . \text { With the load } \\ \text { remaining unchanged, the value of } a \text { is increased by } 10 \% \text { and optimal dispatch is } \\ \left.\text { carried out. The changes in } P_{G 1} \text { and the total cost of generation, } F \text { (= } F_{1}+F_{2}\right) \text { in } \\ \text { Rs/hour will be as follows }\end{array}$ \\
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1. & $P_{G 1}$ will decrease and $F$ will increase \\
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2. & Both $P_{G 1}$ and $F$ will increase \\
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3. & $P_{G 1}$ will increase and $F$ will decrease \\
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4. & Both $P_{G 1}$ and $F$ will decrease \\
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