A system and method for producing argon that uses a higher pressure column, a lower pressure column, and an argon column collectively configured to produce nitrogen, oxygen and argon products through the cryogenic separation of air. The present system and method also employs a once through argon condensing assembly that is disposed entirely within the lower pressure column that is configured to condense an argon rich vapor stream from the argon column against the oxygen-enriched liquid from the higher pressure column to produce an argon liquid product. The control system is configured for optimizing the production of argon product by ensuring an even flow split of the oxygen-enriched liquid is distributed to the argon condenser cores and by adjusting the flow rate of the argon removed from the argon condensing assembly to maintain the liquid/vapor balance in the argon condensing assembly within appropriate limits.