04_03_ex_13.tex

{A power line is to be run to an offshore facility in the manner described in Example \ref{ex_opt3}. The offshore facility is 2 miles at sea and 5 miles along the shoreline from the power plant. It costs \$50,000 per mile to lay a power line underground and \$80,000 to run the line underwater. 

How much of the power line should be run underground to minimize the overall costs?
}
{$5-10/\sqrt{39} \approx 3.4$ miles should be run underground, giving a minimum cost of \$374,899.96.
}