An oil refinery is located on the north bank of a straight river that is 2 km wi
ID: 2828143 • 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
The point P is at 1.154 km along the lower bank i think...
I did this by saying the amount it costs to build is:
2400000-400000*2Tan x +800000 *2/cos x.
or for value of x we can factor down to 3-tan x + 2/cos x.
i.e. Cost of total distance along bank, - excluded section + river crossing section
I graphed this - value for zero between 0 and PI/2 is 0.5235
Tan x = opp / adj so Opp = Tan x * adj giving Opposite of 1.1544 km.