Mathematics: From a tract of land a developer plans to fence a rectangular lot and then divide the lot into 2 identical smaller rectangular lots by putting a fence down the middle of the original lot. suppose that the fence for the outside boundary costs $5 per foot and the fence down the middle costs $2 per foot. if each small lot is to contain 13,500 square feet, calculate the absolute minimum cost for which the fence for this project can be constructed. the absolute minimum value for the cost of constructing

From a tract of land a developer plans to fence a

Ответ:

kitam2871

06.01.2022

Area of the big rectangle:
$xy=27000 
\\y= \frac{27000}{x}$

Total length of the fence:
$\\P=2(x+y)+x
\\P=2x+2y+x
\\P=3x+2y
$

Create function P(x)

:
$\\P(x)=3x+2 \times \frac{27000}{x}
\\P(x)= 3x+ \frac{54000}{x}$

Find the minimum value for

:
$\\P'(x)=3- \frac{54000}{x^2}
\\P'(x)=0
\\3- \frac{54000}{x^2}=0
\\3x^2-54000=0
\\x^2=18000
\\x=\sqrt{18000}
$

Find the minimum value for

:
$\\y= \frac{27000}{x} =\frac{27000}{\sqrt{18000}}$

Calculate the absolute minimum cost for which the fence for this project can be constructed:
$\\C=2(x+y) \times \$5 + x \times \$2
\\C=2(\sqrt{18000}+\frac{27000}{\sqrt{18000}})\times \$5+\sqrt{18000} \times \$2
\\C \approx \$3622} 
$

From a tract of land a developer plans to fence a rectangular lot and then divide the lot into 2 ide

From a tract of land a developer plans to fence a rectangular lot and then divide the lot into 2 ide

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Ответ:

diego4325

17.07.2021

Mathematics

A = π * (r1^2 + r2^2 + (r1 + r2) * s) = π * [ r1^2 + r2^2 + (r1 + r2) * √((r1 - r2)^2 + h2) ]

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