Question 829718
Let {{{ A }}} = area of the field
Let {{{ L }}} = length of the field
Let {{{ W }}} = the width of the field
{{{ A = L*W }}}
{{{ 4800 = 2*9*L + 2*8*W }}}
{{{ 4800 = 18L + 16W }}}
----------------------
I can say;
{{{ L = A/W }}}
and substitute
{{{ 4800 = 18*( A/W ) + 16W }}}
Multiply both sides by {{{ W }}}
{{{ 4800W = 18A + 16W^2 }}}
{{{ 18A = -16W^2 + 4800W }}}
{{{ A = (-8/9)*W^2 + ( 2400/9 )*W }}}
--------------------------------
This is a parabola with a maximum at {{{ W[max] = -b/(2a) }}} where
{{{ a = -8/9 }}}
{{{ b = 800/3 }}}
{{{ W[max] = -( 2400/9 ) / ( 2*( -8/9 ) ) }}}
{{{ W[max] = 2400/16 }}}
{{{ W[max] = 150 }}}
and since
{{{ A[max] = (-8/9)*W^2 + ( 2400/9 )*W }}}
{{{ A[max] = (-8/9)*150^2 + ( 2400/9 )*150 }}}
{{{ A[max] = (-8/9)*22500 + 40000 }}}
{{{ A[max] = -20000 + 40000 }}}
{{{ A[max] = 20000 }}} ft2
check answer:
{{{ 4800 = 18L + 16W }}}
{{{ 4800 = 18L + 16*150 }}}
{{{ 4800 = 18L + 2400 }}}
{{{ 18L = 2400 }}}
{{{ L[max] = 133.333 }}}
{{{ A[max] = W[max]*L[max] }}}
{{{ A[max] = 150*133.333 }}}
{{{ A[max] = 19999.95 }}}
The error is due to rounding off