Consider the points A, B, and C. A company wishes to run a utility cable from point A to point B. Point A lies 9 miles directly east of point C along a straight shoreline. Point B is located on an island 6 miles directly north of point C. It costs $400 per mile to run the cable on land and $500 per mile underwater. Assume that the cable starts at point A and runs along the shoreline, then angles and runs underwater to the island. Find the distance from point A at which the cable line should begin to run underwater in order to yield the minimum total cost.