Question 1062015
The perimeter for 3 sides is 
{{{ P = 2W + L }}}
{{{ L }}} is the side parallel to hwy
{{{ W }}} is perpendicular to hwy
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{{{ P = 600 }}} ft
{{{ 600= 2W + L }}}
{{{ L = 600 - 2W }}}
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The area {{{ A }}} is:
{{{ A = L*W }}}
{{{ A = ( 600 - 2W )*W }}}
{{{ A = -2W^2 + 600W}}}
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{{{ W[max] }}} is found by the formula
{{{ W[max] = -b/(2a) }}}
{{{ a = -2 }}}
{{{ b = 600 }}}
{{{ W[max] = -600/(2*(-2)) }}}
{{{ W[max] = 150 }}} ft
and
{{{ L = 600 - 2W }}}
{{{ L = 600 - 2*150 }}}
{{{ L = 600 - 300 }}}
{{{ L = 300 }}}
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The lot is 150 by 300 ft2
Plug this result back into equation
to find {{{ A[max] }}}
{{{ A[max] = -2*150^2 + 600*150 }}}
{{{ A[max] = -2*22500 + 90000 }}}
{{{ A[max] = -45000 + 90000 }}}
{{{ A[max] = 45000 }}} ft2
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Here's the plot of {{{ A }}} as function of {{{ W }}}
{{{ graph( 400, 400, -50, 350, -5000, 55000, -2x^2 + 600x ) }}}