line constructed from A to island C, 1 mi out from shore B

quipitos

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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
 
Re: max-min problem

quipitos said:
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

First thing draw a picture.
Code:
......................A---------------------D.......B
                                             \
                                               \
                                                 \
                                                   \C

Assume:
The line goes from A to D to C

DB = x

AD = ?

BC = 1

CD = ?

Now write the cost function (C to D and D to A) and minimize it.
 
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