Question 1099767
(a)
Let {{{ W }}} = the length of the 
side perpendicular to the barn
{{{ 2100 - 2W }}} = the length of the side
parallel to the barn
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{{{ A = W*( 2100 - 2W ) }}}
{{{ A = -2W^2 + 2100W }}}
The formula for the W-value of the
maximum is:
{{{ W[max] = -b/(2a) }}}
{{{ a = -2 }}}
{{{ b = 2100 }}}
{{{ W[max] = -2100/( 2*(-2) ) }}}
{{{ W[max] = 525 }}}
and
{{{ 2100 - 2W = 2100 - 2*525 }}}
{{{ 2100 - 1050 = 1050 }}}
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The dimensions that maximize area are:
525 x 1050 
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check:
{{{ A[max] = -2*(W[max])^2 + 2100W[max] }}}
{{{ A[max] = -2*525^2 + 2100*525 }}}
{{{ A[max] = -551250 + 1102500 }}}
{{{ A[max] = 551250 }}} m2
and
{{{ 525*1050 = 551250 }}} m2
OK