Question 1187664
{{{P(x) = -2x^2 + 26x + 44}}}

The company makes a profit when {{{P(x) > 0}}}

{{{-2x^2 + 26x + 44> 0}}}...........simplify

{{{-x^2 + 13x + 22> 0}}}

using quadratic formula we get:{{{ x=(1/2) (13 - sqrt(257))}}} or{{{ x=(1/2) (13 + sqrt(257))}}}

so, {{{P(x) > 0}}} if 

{{{(1/2) (13 - sqrt(257))< x< (1/2) (13 + sqrt(257))}}}........exact solution

approximately

{{{-1.5< x< 14.5 }}}

disregard negative value since {{{P(x) > 0}}}

The company makes a profit when {{{0< x< 14.5 }}}


{{{graph(300,300,-10,20,-20,200,-2x^2+26x+44)}}}