A building with a rectangular base is designed so that the ceiling and the north and south walls lose heat at a rate of 3 units per sq. ft. per day, the east and west walls at a rate of 5 units per sq. ft. per day, and the floor at a rate of 1 unit per sq. ft. per day. Assume that the perimeter of the base cannot exceed 200 feet, and the volume is fixed at 30,000 cu. ft. Find the dimensions for the building that minimizes the heat loss. Specify the domain of your heat loss function and plot it over a rectangular domain that includes the specified domain. Check all points on the interior and the boundary of the domain.