yb1996
  • yb1996
A power line is needed to connect a power station on the shore of a river to a lighthouse 4 km downstream and 1 km off shore. The shoreline is straight. Find the minimum cost for such a line given that it costs $50,000 per km to lay cable underwater and $30,000 per km to lay cable underground.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
|dw:1447199717910:dw|
yb1996
  • yb1996
But that's not minimizing the cost.
anonymous
  • anonymous
I think I did minimize the cost by about $36155.28 by laying down cable across the shore and only 1 km underwater, which is the highest costing cable. BTW, i made a mistake on the dollar sign in the underground cable, it should be $170,000, since it includes both underwater and underground cable

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yb1996
  • yb1996
Sorry, but that can't be right. The cost can be a bit lower if you don't make a right angle with the wiring. Take a look at this: http://webspace.ship.edu/msrenault/GeoGebraCalculus/derivative_app_opt_power.html You have to use calculus to minimize the cost. I just don't know what equation will help me determine the lowest cost.
anonymous
  • anonymous
Refer to the Mathematica attachment. Minimum cost is $160,000 A plot is attached.
1 Attachment
anonymous
  • anonymous
Refer to the attached drawing.
1 Attachment
yb1996
  • yb1996
Thanks. I have been using the equation 30000(4-x) +50000(1+x^2)^(1/2) and I'm getting the wrong answer. You switched the x and the x-4. Is there a reason for that?
anonymous
  • anonymous
The assignment of x to be the distance from the start to the point where the cable went off shore was arbitrary. The solution result should be the same either way.

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