I have the following problem for calculus. It relates to max-min applications of differential equations. My only problem is arriving at the correct equation/function. I know the steps I would need in order to solve for the minimum, I just cannot figure out how to come up with the equation. Could you help? Thanks.
A power line is to be constructed from a power station at point A to an island at point C, which is 1 mile directly out in the water from point B on the shore. Point B is 4 mi downshore from the pwer station at A. It costs $5000 per mile to lay the power line under water and 3000 per mile to lay the line under ground. At what point S downshore from A should the line come to the shore in order to minimize cost? Note that S could very well be B or A
A power line is to be constructed from a power station at point A to an island at point C, which is 1 mile directly out in the water from point B on the shore. Point B is 4 mi downshore from the pwer station at A. It costs $5000 per mile to lay the power line under water and 3000 per mile to lay the line under ground. At what point S downshore from A should the line come to the shore in order to minimize cost? Note that S could very well be B or A