Question 684863
{{{P(x)= -0.001x^2+3x-1800 }}} ...this is a parabola that opens down because {{{a = -0.001}}}, means {{{a < 0}}} and maximum will be at vertex


 {{{-b/2a=-3/2(-0.001)=-3/(-0.002)=1500}}} will give us the {{{x-coordinate}}} of the vertex
 
{{{P(x)= -0.001x^2+3x-1800 }}}...plug in {{{x}}} and find {{{P(x)}}}

{{{P(x)= -0.001(1500)^2+3*1500-1800 }}}

{{{P(x)= -0.001(2250000)+4500-1800 }}}

{{{P(x)= -2250+4500-1800 }}}

{{{P(x)= 4500-4050 }}}

{{{P(x)= 450 }}}

so, global maximum is at ({{{1500}}},{{{450}}})

than 

a) the maximum profits per day is {{{450}}}

b) {{{1500}}}cans must be sold to gain maximum profits

{{{ graph( 700, 700, -100, 2200, -100, 500, -0.001x^2+3x-1800)}}}