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A simple distillation column is designed to separate an ideal binary mixture to specified distillate and bottoms purities at a given column pressure. It $RR_{\text{min}}$ is the minimum reflux ratio for this separation, select the statement that is NOT CORRECT with regard to the variation in the total annualized cost $\text{(TAC)}$ of the column with reflux ratio $\text{(RR)}$.

  1. $\text{TAC}$ has a minimum with respect to $\text{RR}$
  2. The sharpest rise in $\text{TAC}$ occurs as $\text{RR}$ approaches $RR_{\text{min}}$ from above
  3. The sharpest decrease in $\text{TAC}$ occurs as $\text{RR}$ approaches $RR_{\text{min}}$ from above
  4. $\text{TAC}$ increases with $\text{RR}$ for $RR >> RR_{\text{min}}$
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