A factory wants the power company to run a special line to the plant. The power company is located 1000 meters down a river on the opposite bank. Ground lines cost $20 per meter. The river is 500 meters wide and underwater line will cost M (M> 1) times as much per meter as the above ground line. Since the factory owns the riverfront property on both sides of the river all the way to the power plant, you may choose where and how the line should cross the river.

1- Find in terms of M all paths that will minimize the cost and what the minimum cost is. Be sure to describe your paths clearly. See diagram.

2- If M =50 give the minimum cost and the best path.

3- If M =2 give the minimum cost and the best path.

4- If M =1.05 give the minimum cost and the best path.