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Answer: An oil refinery is located on the north bank of a straight river that is 2 km
Chapter 4, Problem 51(choose chapter or problem)
An oil refinery is located on the north bank of a straight river that is 2 km wide. A pipeline is to be constructed from the refinery to storage tanks located on the south bank of the river 6 km east of the refinery. The cost of laying pipe is $400,000ykm over land to a point \(P\) on the north bank and $800,000ykm under the river to the tanks. To minimize the cost of the pipeline, where should \(P\) be located?
Questions & Answers
QUESTION:
An oil refinery is located on the north bank of a straight river that is 2 km wide. A pipeline is to be constructed from the refinery to storage tanks located on the south bank of the river 6 km east of the refinery. The cost of laying pipe is $400,000ykm over land to a point \(P\) on the north bank and $800,000ykm under the river to the tanks. To minimize the cost of the pipeline, where should \(P\) be located?
ANSWER:Step 1 of 3
Let x denote the distance (in km) between the refinery and the point p on the north bank at which the underwater pipeline begins we only consider 
The cost of laying pipe between the refinery and point p (in hundreds of thousands of dollars) is 4x.By the pythagorean theorem the length of the underwater pipeline between p and storage tank is 
We now need to find the value of x for which the total cost is minimal. We have
In order that 
This equivalent to
Squaring both sides of the equation gives 
writing this quadratic equation in standard form , we have 
using the quadratic formula gives 