A telecommunications company needs to install a fiber optic cable from a central office to a new development $3$ miles away on the opposite side of a lake. The lake is $1200$ ft wide. The cost of laying the cable under the lake is $$250$ per foot and $$150$ per foot along the road. Determine the least expensive point for the cable to reach the development if it is less than or greater than $3000$ ft from the starting point along the road.