An island is 3 mi from the nearest point on a straight shoreline; that point is 14 mi from a power station (see figure). A Utility company plans to lay electrical cable underwater from the island to the shore and then underground along the shore to the power station. Assume that is costs $3200/mi to lay cable underwater and $1600/mi to lay underground cable. At what point should the underwater cable meet C=| the shore to minimize the cost of the project? Write an equation for the total cost, C, as a function of x, where x is the distance from the shoreline closest to the island and the point where the cable leaves the shore. (Type an expression.) Island The interval of interest of the objective function is (Simplify your answer. Type your answer in interval notation.) Cable 3 mi The cost is minimized when x is mi. Power Station (Type an exact answer.) 14 mi The minimum installation cost is $. (Round to the nearest cent as needed.)
An island is 3 mi from the nearest point on a straight shoreline; that point is 14 mi from a power station (see figure). A Utility company plans to lay electrical cable underwater from the island to the shore and then underground along the shore to the power station. Assume that is costs $3200/mi to lay cable underwater and $1600/mi to lay underground cable. At what point should the underwater cable meet C=| the shore to minimize the cost of the project? Write an equation for the total cost, C, as a function of x, where x is the distance from the shoreline closest to the island and the point where the cable leaves the shore. (Type an expression.) Island The interval of interest of the objective function is (Simplify your answer. Type your answer in interval notation.) Cable 3 mi The cost is minimized when x is mi. Power Station (Type an exact answer.) 14 mi The minimum installation cost is $. (Round to the nearest cent as needed.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:An island is 3 mi from the nearest point on a straight shoreline; that point is 14 mi
from a power station (see figure). A Utility company plans to lay electrical cable
underwater from the island to the shore and then underground along the shore to
the power station. Assume that is costs $3200/mi to lay cable underwater and
$1600/mi to lay underground cable. At what point should the underwater cable meet
the shore to minimize the cost of the project?
Write an equation for the total cost, C, as a function of x, where x is the distance
from the shoreline closest to the island and the point where the cable leaves the
shore.
C =
(Type an expression.)
Island
The interval of interest of the objective function is
Cable
(Simplify your answer. Type your answer in interval notation.)
3 mi
The cost is minimized when x is
mi.
Power
Station
(Type an exact answer.)
14 mi
The minimum installation cost is $
(Round to the nearest cent as needed.)
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