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The Annual Fixed Charges ($AFC$) and Annual Utilities Costs ($AUC$) of a distillation column being designed are expressed in terms of the reflux ratio ($R$) as

$AFC$ ($Rs.$ Lakh) = $641\times R^{2}-1796\times R+1287+1/\left ( R-1.16 \right )$

$AUC$ ($Rs.$ Lakh) = $80+62.5\times R$

The reflux ratio ($R_{opt}$) for optimizing the total cast of the distillation column may be found by solving

- $1282\times R_{opt}-1796-1/\left ( R_{opt} -1.16\right )^{2}=0$
- $62.5+1282\times R_{opt}-1796-1/\left ( R_{opt} -1.16\right )^{2}=0$
- $80+62.5\times R_{opt}+641\times R_{opt}^{2}-1796\times R_{opt}+1287+1/\left ( R_{opt} -1.16\right )=0$
- $80+62.5\times R_{opt}-641\times R_{opt}^{2}+1796\times R_{opt}-1287-1/\left ( R_{opt} -1.16\right )=0$