An oil refinery is located on the north bank of a straight river that is 2 km wi
ID: 2828146 • Letter: A
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 $400,000/km over land and $800,000/km under the river. To minimize the cost of the pipeline, to what point P on the south bank should the pipe come out of the river? (Draw a picture of the problem and show your point P. Note: time has nothing to do with this problem.)
Explanation / Answer
You should draw this out. The pipeline will go horizontally east for some distance and then go through the water at a diagonal. The total horizontal distance will be 6 km, and the total vertical distance will be 2 km.
let x be the horizontal distance, and y be the diagonal distance.
the cost, in hundred-thousands, will be
C = 4x+8y
and from the pythagorean theorem,
y