Sherman Corporation produces chemical Hawthorne in batches of 10,000 gallons. Typically, the raw materials for a batch cost $38,000 and processing cost is $46,000, resulting a cost of $8.40/gallon. Hawthorne can be sold for $11/gallon, or processed further into Fillmore at a cost of $32,000 per batch. This processing results in 9,500 gallons of Fillmore (the other 500 gallons are waste necessitated by the nature of the chemical process). Fillmore can be sold for $16/gallon. Should Sherman sell Hawthorne or process further into Fillmore? Explain and show necessary calculations.