A contractor builds two types of homes. The Carolina requires one lot, $160,000 capital, and 160 worker-days of labor, and 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.
(a) Write the simplex matrix to maximize the profit.
(b) Use the simplex method to find how many of each type of home should be built to maximize profit, and find the maximum possible profit.