38. Refining A refinery has two smelters that extract metallic iron from iron ore. Smelter A processes 1000 tons of iron ore per
hour and uses 7 megawatts of energy per hour. Smelter B pro-
cesses 2000 tons of iron ore per hour and uses 13 megawatts
of energy per hour. Each refinery must be operated at least
8 hours per day and, of course, no more than 24 hours. If
the refinery must process at least 30,000 tons of iron ore per
day, how many hours should each smelter operate in order to
expend as little energy as possible?