A builder has $6 million and 12 acres of land on which to build cottages, ranch houses, and McMansions. Each cottage requires 1/4 acre of land and $100,000 to build, and yields a profit of $6000. Each ranch house requires 1/2 acre of land and $400,000 to build, and yields a profit of $13,000. Each McMansion requires 1 acre of land and $200,000 to build, and yields a profit of $14,000. How many houses of each type should be built in order to maximize the profit?