CEMEX and Holcim are two cement manufacturers in Durham. They produce cement and sell it into a competitive world market at the fixed price of $60 per ton. Producing one ton of cement also produces one ton of air pollution that negatively impacts Durham. Suppose that the one-to-one relationship between cement and pollution production is immutable at both factories. The total cost to CEMEX of producing QC units of cement is 500 + (QC)^2 and the total cost to Holcim of producing QH units of cement is 300 + 2(QH)^2. Total pollution is EC + EH = QC + QH. Marginal damages from pollution are equal to $12 per ton of pollution.

In the absence of regulation, how much cement does each firm produce? What are the profits for each firm? And what is total production and total profit?