ANS:A - minimum

The operating cost of a distillation column at minimum reflux ratio is maximum. Explanation:

• The reflux ratio in a distillation column refers to the ratio of the liquid returned to the top of the column (reflux) to the liquid withdrawn as product.
• At minimum reflux ratio, the amount of liquid returned to the column is minimized, meaning that the ratio of reflux to product is minimized.
• Operating a distillation column at minimum reflux ratio typically results in less efficient separation of the desired components from the feed mixture.
• To achieve the desired separation with lower reflux ratios, the column may require additional trays or stages and/or higher energy input, such as increased reboiler heat input, to maintain separation efficiency.
• These additional requirements lead to higher operating costs, including energy consumption, maintenance, and potentially higher capital costs for equipment modifications.
• Therefore, the operating cost of a distillation column at minimum reflux ratio is typically maximum compared to operation at higher reflux ratios where separation efficiency is greater and operating conditions are more optimized.

In summary, while minimum reflux ratio operation may reduce the amount of reflux liquid used, it often leads to decreased separation efficiency and increased operating costs, making it typically the most expensive operating condition for a distillation column.