.An internet provider needs to run an underground cable from station A, on one side of a river, to station C on the other side of the river. The river is 300 meters across (the shortest way) and station C is 400 meters along the river to a point directly across from station A (see diagram). Laying the cable costs $100 per meter under dry ground, and $200 per meter under the river. The company will lay the cable under the ground along the river until it gets to point B (which is a distance x from A), and then lay the cable in a straight line under the river from B to C. How far apart should point B be from station A in order to minimize the cost of laying the cable? Hint: Label a point D directly across the river from B, and write the objective function in terms of the distance from D to C.

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3. An internet provider needs to run an underground cable from station A, on one side
of a river, to station C on the other side of the river. The river is 300 meters across
(the shortest way) and station C is 400 meters along the river to a point directly across
from station A (see diagram).
Laying the cable costs $100 per meter under dry ground, and $200 per meter under the
river.
The company will lay the cable under the ground along the river until it gets to point
B (which is a distance x from A), and then lay the cable in a straight line under the
river from B to C. How far apart should point B be from station A in order to minimize
the cost of laying the cable?
Hint: Label a point D directly across the river from B, and write the objective function
in terms of the distance from D to C.
400 m
300 m
A
В
Transcribed Image Text:3. An internet provider needs to run an underground cable from station A, on one side of a river, to station C on the other side of the river. The river is 300 meters across (the shortest way) and station C is 400 meters along the river to a point directly across from station A (see diagram). Laying the cable costs $100 per meter under dry ground, and $200 per meter under the river. The company will lay the cable under the ground along the river until it gets to point B (which is a distance x from A), and then lay the cable in a straight line under the river from B to C. How far apart should point B be from station A in order to minimize the cost of laying the cable? Hint: Label a point D directly across the river from B, and write the objective function in terms of the distance from D to C. 400 m 300 m A В
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