A factory is located on one bank of a straight river that is 2000 m wide. On the opposite bank but 4500 m downstream is a power station from which the factory draws its electricity. Assume that it costs $3 per meter to lay an underwater cable and $1 per meter to lay an above ground cable.

Question

A factory is located on one bank of a straight river that is 2000 m wide. On the opposite bank but 4500 m downstream is a power station from which the factory draws its electricity. Assume that it costs $3 per meter to lay an underwater cable and $1 per meter to lay an above ground cable.
How long should the cable above ground be in order to minimize the total cost?

Steve · Answer

If the cable comes out of the river x meters from the point directly opposite the factory, then the cost is c = 3√(x^2+2000^2) + 1(4500-x) so, find where dc/dx=0 The answer is 4500-x.