Infinite Sequences and Series · Hard problem

A recycling plant receives a shipment of $M$ kg of aluminum at the start of each cycle. By the start of the next cycle, only $20\%$ of the previous cycle's stockpile remains (the rest having been processed), and this repeats forever, so the stockpile right after each new shipment approaches a steady long-run level. If that long-run level is exactly $600$ kg, find $M$.