Question 691277
The minus in front of the {{{ x^2 }}} term
means there is a max and not a min.
{{{ P = -25x^2 + 300x }}}
{{{ P = x*( 300 - 25x ) }}}
Set {{{ P=0 }}} to find roots
the roots are
{{{ x = 0 }}}
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{{{ 300 - 25x = 0 }}}
{{{ 25x = 300 }}}
{{{ x = 12 }}}
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The  x-coordinate of the maximum 
is midway between the roots
{{{ ( 0 + 12 ) / 2 = 6 }}}
So {{{ x = 6 }}} is the maximum
Now find {{{P}}} at {{{ x=6 }}}
{{{ P = -25*6^2 + 300*6 }}}
{{{ P = -900 + 1800 }}}
{{{ P = 900 }}}
With 6 clerks working that day, there is
a maximum profit of $900
here's a plot:
{{{ graph( 400, 400, -2, 15, -50, 1000 , -25x^2 + 300x ) }}}