Question

An island is 3 mi from the nearest point on a straight​ shoreline; that point is 6 mi from a power station​. 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 that is costs ​2800​/mi to lay cable underwater and ​$1400​/mi to lay underground cable. At what point should the underwater cable meet the shore to minimize the cost of the project. Write an equation for the total​ cost, C​, as a function of​ x, where x is the distance from the shoreline closest to the island and the point where the cable leaves the shore. Find interval of interest, the mi where cost is minimized, and minimum installation cost.

Answer 1

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