Solve the following Linear Programming problems using The Simplex Method. Show all work. Write a sentence answer.

1.) 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 $24000. The second type of home requires one lot, $32,000 capital, and 200 labor-days to build and is sold for a profit of $34000. 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?

2.) A Freight company handles shipments by two corporations, A and B, which are located in the same city. Corporation A ships boxes that weigh 3 lbs each and have a volume of 2 cu ft. Corporation B ships 1 cu ft. boxes that weigh 5 lbs each. Both A and B ship to the same destination. The transportation cost to the customer (price) for each box from A is $0.75, and from B is $0.50. The freight company has a truck with 2400 cu ft. of cargo space and a maximum capacity of 9200 lbs. In one haul, how many boxes from each corporation should be transported by this truck so that the freight company receives maximum revenue? What is the maximum revenue?