A small resort is situated on an island off a part of the coast of Mexico that has a perfectly straight north-south shoreline. The point P on the shoreline that is closest to the island is exactly 3 miles from the island. Ten miles south of P is the closest source of fresh water to the island.

A pipeline is to be built from the island to the source of fresh water by laying pipe underwater in a straight line from the island to a point Q on the shoreline between P and the water source, and then laying pipe on land along the shoreline from Q to the source. It costs 2 times as much money to lay pipe in the water as it does on land. How far south of P should Q be located in order to minimize the total construction costs?

Hint: You can do this problem by assuming that it costs one dollar per mile to lay pipe on land, and 2 dollars per mile to lay pipe in the water. You then need to minimize the cost over the interval [0,10] of the possible distances from P to Q.

Distance from P = miles.