Question 881296
Let {{{ L }}} = length of the garden in feet
Let {{{ W }}} = width of the garden in feet
Let {{{ A }}} = the area of the garden in ft2
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(1) {{{ 14W + 9W + 2*9*L = 828 }}}
(1) {{{ 23W + 18L = 828 }}}
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(2) {{{ A = W*L }}}
from (1):
(1) {{{ 18L = 828 - 23W }}}
(1) {{{ L = 46 - (23/18)*W }}}
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By substitution:
(2) {{{ A = W*( 46 - (23/18)*W ) }}}
(2) {{{ A = 46W - (23/18)*W^2 }}}
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I can say then:
(2) {{{ f(W) = -(23/18)*W^2 + 46W }}}
The maximum occurs at:
{{{ W[max] = -b/(2a) }}}
{{{ -b/(2a) = -46/(-23/9) }}}
{{{ -b/(2a) = 18 }}} 
{{{ W[max] = 18 }}}
Plug this back into (1)
(1) {{{ 23*18 + 18L = 828 }}}
(1) {{{ 414 + 18L = 828 }}}
(1) {{{ 18L = 414 }}}
(1) {{{ L = 23 }}}
and
(2) {{{ A = W*L }}}
(2) {{{ A[max] = 18*23 }}}
(2) {{{ A[max] = 414 }}} 
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The cedar side is 18 ft
The maximum area is 414 ft2
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Here's the plot:
{{{ graph( 400, 400, -5, 50, -40, 450, -(23/18)*x^2 + 46x ) }}}