Question 912653
{{{ x[max] = -b/(2a) }}}
where:
{{{ a = -1 }}}
{{{ b = 22 }}}
{{{ x[max] = -22/(2*(-1)) }}}
{{{ x[max] = 11 }}}
------------------
{{{ P[max] = -11^2 + 22*11 - 18 }}}
{{{ P[max] = -121 + 242 - 18 }}}
{{{ P[max] = 103 }}}
------------------
{{{ 40 = -x^2 + 22x - 18 }}}
{{{ x^2 - 22x = -58 }}}
Complete the square
{{{ x^2 - 22x + (22/2)^2 = -58 + (22/2)^2 }}}
{{{ x^2 - 22x + 121 = -58 + 121 }}}
{{{ x^2 - 22x + 121 = 63 }}}
{{{ ( x - 11 )^2 = 63 }}}
Take the square root of both sides
{{{ x - 11 = 3*sqrt(7) }}}
{{{ x = 11 - 7.9373 }}}
{{{ x = 3.0627 }}}
and
{{{ x = 11 + 7.9373 }}}
{{{ x = 18.9373 }}}
------------------
More than 3,063 units and less than 18,937
units should be produced
-----------------
check my math, too