Chapter 4.5, Problem 29E

Laying cable again Solve the problem in Exercise 28, but this time minimize the cost with respect to the smaller angle θ between the underwater cable and the shore. (You should get the same answer.)

28.    Laying cable An island is 3.5 mi from the nearest point on a straight shoreline; that point is 8 mi from a power station (see figure). A utility company plans to lay electrical cable underwater from the island to the shore and then underground along the shore to the power station. Assume it costs $2400/mi to lay underwater cable and $1200/mi to lay underground cable. At what point should the underwater cable meet the shore in order to minimize the cost of the project?