Minimizing Power Line Costs. A power line is constructed from a power station at point A t...

Minimizing Power Line Costs. A power line is constructed from a power station at point A to an island at point I, which is 1 mi directly out in the water from a point B on the shore. Point B is 4 mi downshore from the power station at A. It costs $5000 per mile to lay the power line under water and $3000 per mile to lay the power line under ground. The line comes to the shore at point S downshore from A. Let x = the distance from B to S.

a) Express the cost C of laying the line as a function of x.

b) At what distance x from point B should the line come to shore in order to minimize cost?