An island is 3 mi from the nearest point on a straight shoreline; that point is 13 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 $2800imi to lay cable underwater and $1400imi 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- 2800 (9+) + 1400(13 - x) Iland (Type an expression.) Cable The interval of interest of the objective function is [0,13] (Simplify your answer. Type your answer in interval notation.) Station The cost is minimized when x is 3 mi. (Type an exact answer) -13 mi The minimum installation cost is S (Round to the nearest cent as needed.)
An island is 3 mi from the nearest point on a straight shoreline; that point is 13 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 $2800imi to lay cable underwater and $1400imi 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- 2800 (9+) + 1400(13 - x) Iland (Type an expression.) Cable The interval of interest of the objective function is [0,13] (Simplify your answer. Type your answer in interval notation.) Station The cost is minimized when x is 3 mi. (Type an exact answer) -13 mi The minimum installation cost is S (Round to the nearest cent as needed.)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
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Chapter5: A Survey Of Other Common Functions
Section5.2: Power Functions
Problem 17E: Tsunami Waves and BreakwatersThis is a continuation of Exercise 16. Breakwaters affect wave height...
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![4.5.28
D Assigned Media
E Question Help
An island is 3 mi from the nearest point on a straight shoreline; that point is 13 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 $2800/mi to lay cable underwater and
$1400/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= 2800 (/9 +x) + 1400(13 – x)
Island
(Type an expression.)
Cable
The interval of interest of the objective function is [0,13] .
3 mi
Power
Station
(Simplify your answer. Type your answer in interval notation.)
The cost is minimized when x is 3 mi.
13 mi
(Type an exact answer.)
The minimum installation cost is $
(Round to the nearest cent as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F73bbbd69-dae2-4a6d-9048-6b183e7673d6%2Fb2737f8d-3302-45d9-be29-a171af5b19de%2F7fn0j2o_processed.png&w=3840&q=75)
Transcribed Image Text:4.5.28
D Assigned Media
E Question Help
An island is 3 mi from the nearest point on a straight shoreline; that point is 13 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 $2800/mi to lay cable underwater and
$1400/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= 2800 (/9 +x) + 1400(13 – x)
Island
(Type an expression.)
Cable
The interval of interest of the objective function is [0,13] .
3 mi
Power
Station
(Simplify your answer. Type your answer in interval notation.)
The cost is minimized when x is 3 mi.
13 mi
(Type an exact answer.)
The minimum installation cost is $
(Round to the nearest cent as needed.)
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