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 5 km east of the refinery. The cost of laying pipe is $200,000/km over land to a point P on the north bank and $400,000/km under the river to the tanks. To minimize the cost of the pipeline, how far from the refinery should P be located? (Round your answer to two decimal places.) km

Answer 1

Answer:

5.39km

Step-by-step explanation:

Using right angle triangle to model the distance between the north location of the refinery and the south 5km east of the p the storage tank, let p represent the location and hypothenus of the triangle and the others to 2km the width of the river and 5km east of south of the refinery.

Using Pythagoras theorem

Hyp^2 = 2^2 + 5^2 = 4+25 = 29

Hyp(the distance of p to the north part where the refinery is ) = √29 = 5.39km to the refinery and the angle will be tan (angle) = 2/5

Angle = tan^-1 0.4 = 21.8 to the horizontal