Question 737640
A farmer wishes to make three equal sized rectangular corrals.
 The outside fence costs $3/ft and the inside fence costs $1/ft.
 If he has $1200 to spend on the corrals, what dimensions will provide the corrals of greatest area?
:
The fence consists of 3 widths and 2 lengths, one width will cost $1 a foot
the other two cost $3, as does the 2 lengths
:
3(2L) + 3(2W) + 1(W) = 1200
6L + 6W + W = 1200
6L + 7W = 1200
6L = 1200-7W
L = {{{(1200-7W)/6}}}
:
Area = L * W
replace L
A = {{{(1200-7W)/6}}} * W
A = {{{(1200W-7W^2)/6}}}
divide both coefficients by 6, write it as a quadratic equation 
A = {{{-7/6}}}W^2 + 200W
Max area occurs on the axis of symmetry, find that with x =-b/(2a)
w = {{{-200/(2*(-7/6))}}}
using decimals here
w = {{{(-200)/-2.33}}}
w ~ 85.7 ft is the width
Find the length
L = {{{(1200-7(85.7))/6}}}
do the math
L ~ 100 ft is length for max area for $1200
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You should check this out for math errors