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.
Stacey Warren - Expert brainly.com
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But that's not minimizing the cost.
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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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.
Refer to the Mathematica attachment.
Minimum cost is $160,000
A plot is attached.