Need urgent help!!

shea

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Dec 15, 2005
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Piping Oil from a drilling Rig to a refinery

A drilling rig 12 mi offshore is to be connected by pipe to a refinery onshore, 20 mi straight down the coast from the rig. If underwater pipe costs $50,000 per mile and land-based pipe costs $30,000 per mile, what combination of the two will give the least expensive connection.

How could you find it and what's the best we can do.

My teacher mentioned something about using an equation, with graphs and using DERIVATIVES,
 
You pick a spot x miles down the coast where the pipe comes ashore. Underwater pipe runs
sqrt(12²+x²) miles
Land pipe runs 20-x miles.
Cost = 50sqrt(12²+x²)+30(20-x) thousand dollars.
Set dC/dx = 0 then solve for x.
 
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