No. Using your measurements, that would mean they lay the cable underwater in a straight line from the Lighthouse to the point A, and then lay shoreline cable from A to B. Draw that on a piece of paper; you will see you get a right triangle. What is smaller the Hypotenuse, or the 12KM+4KM?

$48,000 is going to be your maximum cost, but we want the OPTIMIZATION of this situation; in that we want the MINIMUM cost, and the corresponding distance of C from A that relates to that.

The distance I got from A to C was

. Hopefully I did that right, and perhaps someone can hop in and check.