Question 1150524
Let the side perpendicular to the highway = {{{ w }}}
{{{ 500 - 2w }}} = the length of the side parallel to the highway
Let {{{ A }}} = the area of the lot
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{{{ A = w*( 500 - 2w ) }}} 
{{{ A = -2w^2 + 500w }}}
Use the formula for the vertex:
{{{ w[pk] = -500/( 2*(-2)) }}}
{{{ w[pk] = 125 }}}
Plug this result back into equation
{{{ A[max] = -2*(125)^2 + 500*125 }}}
{{{ A[max] = 31250 }}} ft2
Since 40000 ft2 is greater than the maximum area
this can't be enclosed with 500 ft of fencing
Here's the plot:
{{{ graph( 400, 400, -100, 300, -3500, 35000, -2x^2 + 500x ) }}}