A contractor builds two types of homes. The Carolina requires one lot, $160,000 capital, and 160 worker-days of labor, whereas the Savannah requires one lot, $240,000 capital, and 160 worker-days of labor. The contractor owns 300 lots and has $48,000,000 available capital and 43,200 worker-days of labor. The profit on the Carolina is $40,000 and the profit on the Savannah is $50,000. Find how many of each type of home should be built to maximize profit. Find the maximum possible profit.