Question 373686
A farmer wishes to fence off three identical adjoining rectangular pens,
 each with 1000 sq/ft of area. 
What are dimensions so that the least amount of fence is required?
:
Total area: 3(1000) = 3000 sq/ft
:
Area:
L * w = 3000
L = {{{3000/w}}}
:
Three adjoining pens
___L__
|_|_|_|w
:
Perimeter (length of fence)
F = 2L + 4w
Replace L with {{{3000/w}}}
F = 2({{{3000/w}}}) + 4w
F = {{{6000/w}}} + 4w
:
Find the minimum fencing by graphing this equation: y = {{{6000/x}}} + 4x
{{{ graph( 300, 200, -20, 100, -200, 500, (6000/x)+4x) }}}
You can see minimum occurs when x = 40
:
Find L: L = {{{3000/40}}} = 75 ft is the length
:
Overall dimensions of 75 ft by 40 ft for minimum fencing
:
:
Check: each pen: 25*40 = 1000 sq/ft


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