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 ref
inery to storage tanks located on the south bank of the river 10 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.)
1 answer:
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Answer:
Step-by-step explanation:
Given
Empty Tank
When filled with water, the height is:
Required
Determine how many more cubic inches needed
First, we calculate the difference between the height of the tank and the height of the water.
The volume of water to full the tank is then calculated as:
The graph suggests that the two lines meet at
If this is true, that point must belong to both lines.
To check this, plug in both equations, and you must get
once you simplifiy all the numbers.
In the first equation we have
In the second,