A contractor builds two types of homes. The first type requires one lot, $12,000 capital, and 150 labor-days to build and is sold for a profit of $2,400. The second type of home requires one lot, $32,000 capital, and 200 labor-days to build and is sold for a profit of $3,400. The contractor owns 150 lots and has available for the job $2,880,000 capital and 24,000 labor-days. How many homes of each type should she build to realize the greatest profit?

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