A resort is situated on an island that lies exactly 4 miles from P, the closest point to the island along a perfectly straight shoreline. 10 miles dow

EunoR

EunoR

Answered question

2020-11-08

A resort is situated on an island that lies exactly 4 miles from P, the closest point to the island along a perfectly straight shoreline. 10 miles down the shoreline from P is the nearest source of water. If it costs 1.6 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 with minimum total constructions costs?

Answer & Explanation

Luvottoq

Luvottoq

Skilled2020-11-09Added 95 answers

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 1,6 times.
If x is at distance y from P, then the cost of pipeline
C=(10y)+1.6y2+42
dcdy=1+1.6yy2+16
dcdy=0
y2+16=1.6y
y2+16=2.56y2
16=1.56y2
y=3.202
Distance from P is 3.202 miles

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