Question 1177769
{{{P(x)=1+8x-2x^2}}}

max is at vertex

complete square and find coordinates of the vertex

{{{P(x)=-2x^2+8x+1}}}

{{{P(x)=-2(x^2-4x)+1}}}
{{{P(x)=-2(x^2-4x+2^2)-(-2)(2^2)+1}}}
{{{P(x)=-2(x-2)^2+8+1}}}
{{{P(x)=-2(x-2)^2+9}}}

=>  {{{h=2 }}}and {{{k=9}}}

vertex is at ({{{2}}},{{{9}}})

so, {{{x=2}}} which means  {{{2000}}} Boombotix speakers should be sold to maximize profit