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?

Answers

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.

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