Asked by Anonymous

A small resort is situated on an island that lies exactly 6 miles from P, the nearest point to the island along a perfectly straight shoreline. 10 miles down the shoreline from P is the closest source of fresh water. If it costs 1.4 times as much money to lay pipe in the water as it does on land, how far down the shoreline from P should the pipe from the island reach land in order to minimize the total construction costs?

Answers

Answered by Steve
P=point on shore
R=resort
W=water source
X=point on shore where pipe enters water
Assume land pipe costs 1, water pipe costs 1.4

If X is at distance x from P, then
the cost of the pipeline

c = (10-x)+1.4sqrt(x^2+36)
dc/dx = -1 + 1.4x/sqrt(x^2+36)
dc/dx = 0 where

sqrt(x^2+36) = 1.4x
x^2+36 = 1.96x^2
.96x^2 = 36
x^2 = 37.5
x = 6.12
Answered by H H Chau
Concur.
Answered by K
I tried this and it didn't work for my problem even though they were exactly the same except for the 1.4 in this problem being 2.9 in mine.
Answered by Trash Panda
That would be because they missed the 2 in the denominator for their:
c = (10-x)+1.4sqrt(x^2+36)
dc/dx = -1 + 1.4x/sqrt(x^2+36)


it should actually be:
dc/dx = -1 + 1.4/2*sqrt(x^2+36)
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