A power station A and sub-station B are separated by hills. The shortest distance through the hills is 12.0 km due north. The distance from A to this point is 18.0 km due west over level ground. Underground power cabling is needed to connect A and B. At some stage the cable must run through the hills to get to B which is located immediately on the other side of the hills. The cost of laying the cable on level land is £175,000 per km. The cost of tunnelling it through hill is £550,000 per km. a. Using differential calculus find the most economical way of laying the pipeline from A to B and the length of tunnelling required. Verify that it is a minimum value by used of a calculus method. b. Check your solutions in a by using a graphical method and compare your answers.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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A power station A and sub-station B are separated by hills. The shortest
distance through the hills is 12.0 km due north. The distance from A to
this point is 18.0 km due west over level ground. Underground power
cabling is needed to connect A and B. At some stage the cable must run
through the hills to get to B which is located immediately on the other
side of the hills.
The cost of laying the cable on level land is £175,000 per km. The cost of
tunnelling it through hill is £550,000 per km.
B
A
a. Using differential calculus find the most economical way of laying
the pipeline from A to B and the length of tunnelling required.
Verify that it is a minimum value by used of a calculus method.
b. Check your solutions in a by using a graphical method and
compare your answers.
Transcribed Image Text:A power station A and sub-station B are separated by hills. The shortest distance through the hills is 12.0 km due north. The distance from A to this point is 18.0 km due west over level ground. Underground power cabling is needed to connect A and B. At some stage the cable must run through the hills to get to B which is located immediately on the other side of the hills. The cost of laying the cable on level land is £175,000 per km. The cost of tunnelling it through hill is £550,000 per km. B A a. Using differential calculus find the most economical way of laying the pipeline from A to B and the length of tunnelling required. Verify that it is a minimum value by used of a calculus method. b. Check your solutions in a by using a graphical method and compare your answers.
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