A pipeline is to be built from a point on the bank of an 800m wide river to a point 3km downstream on the opposite bank. a) The building costs for the pipeline are $750,000 per km under the river and $250,000 per km over the land. By using the information on the diagram show that the cost (C) of the pipeline can be given by: C = 750000 (√y² +0.64+1) - 250000y b) Find the value of y that minimizes the cost. c) Verify that the value for y that you have found minimizes the cost. d) What is the minimum cost of building the pipeline? River B X A
A pipeline is to be built from a point on the bank of an 800m wide river to a point 3km downstream on the opposite bank. a) The building costs for the pipeline are $750,000 per km under the river and $250,000 per km over the land. By using the information on the diagram show that the cost (C) of the pipeline can be given by: C = 750000 (√y² +0.64+1) - 250000y b) Find the value of y that minimizes the cost. c) Verify that the value for y that you have found minimizes the cost. d) What is the minimum cost of building the pipeline? River B X A
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:16. A pipeline is to be built from a point on the bank of an 800m wide river to a point
3km downstream on the opposite bank.
a) The building costs for the pipeline are $750,000 per km under the
river and $250,000 per km over the land.
By using the information on the diagram show that the cost (C) of
the pipeline can be given by:
C = 750000 (√y² +0.64 + 1) - 250000y
b)
Find the value of y that minimizes the cost.
c) Verify that the value for y that you have found minimizes the cost.
d) What is the minimum cost of building the pipeline?
River
B
X
y
A
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