Question: A cable company is to run an optical cable from a relay station, A, on the shore to an installation, B, on an island, as

A cable company is to run an optical cable from a relay station, A, on the shore to an installation, B, on an island, as shown in Figure 1.33. The island is 6 km from the shore at its nearest point, P, and A is 9 km from P measured along the shore. It is proposed to run the cable from A along the shoreline and then underwater to the island. It costs 25% more to run the cable underwater than along the shoreline. At what point should the cable leave the shore in order to minimize the total cost?

Figure 1.33

B 6 km P x km 9 km D HA

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