A farmer wants to enclose a rectangle shaped field the size of 6000 ft^2 on his farm adjacent to a river. His plan is to divide the field into 4 sections. He does not need a fence along the river. His neighbor will pay half the price of the fence bordering the 2 properties. The farmer wants a strong fence on the south side that costs $10 a foot, and a cheap fence for the rest that cost $8 a foot. Find the dimensions of the field that minimize the cost of building the fence. Picture of the fence is below.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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A farmer wants to enclose a rectangle shaped field the size of 6000 ft^2 on his farm adjacent to a river. His plan is to divide the field into 4 sections. He does not need a fence along the river. His neighbor will pay half the price of the fence bordering the 2 properties. The farmer wants a strong fence on the south side that costs $10 a foot, and a cheap fence for the rest that cost $8 a foot. Find the dimensions of the field that minimize the cost of building the fence.

Picture of the fence is below.

river
south
neighbor
Transcribed Image Text:river south neighbor
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