Question

An oil refinery is located 1 km north of 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 5 km east of the refinery. The cost of laying pipe is $300,000/km over land to a point P on the north bank and $600,000/km under the river to the tanks. To minimize the cost of the pipeline, how far downriver from the refinery should the point P be located? (Round your answer to two decimal places.)

Answer 1

Answer:

The point p should be located to 4.42 km far from the refinery

Explanation:

Minimum of these costs occurs when x = 1/$\sqrt{3}$ , so distance should be m km to the east of the refinery.

m = 5 - x

m = 5 - 1/$\sqrt{3}$

m = 4.42 km