Question 943355
{{{P(x) = -0.8x^2 + 16.2x - 10}}}
where {{{0 <= x <= 22 }}}

to find the breakeven point for this problem, set {{{P(x) = 0}}} and solve for {{{x}}}

{{{0= -0.8x^2 + 16.2x - 10}}} ...multiply all terms by {{{10}}} to get rid of decimals

{{{0= -8x^2 + 162x - 100}}}

{{{0= -2(4x^2 - 81x + 50)}}} this product will be equal to {{{0}}} if

{{{0= (4x^2 - 81x + 50)}}} ...use quadratic formula to find {{{x}}}


{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}


{{{x = (-(-81) +- sqrt( (-81) ^2-4*4*50 ))/(2*4) }}}


{{{x = (81 +- sqrt( 6561-800 ))/8 }}}


{{{x = (81 +- sqrt( 5761 ))/8 }}}


{{{x = (81 +- 75.9)/8 }}}

solutions:

{{{x = (81 + 75.9)/8 }}}

{{{x = 156.9/8 }}}

{{{highlight(x =19.6)}}}

or

{{{x = (81 - 75.9)/8 }}}

{{{x = 5.1/8 }}}

{{{highlight(x =0.6)}}}


so,  both solutions satisfy given condition {{{0 <= x <= 22 }}}

{{{0 <= 19.6 <= 22 }}}
{{{0 <= 0.6 <= 22 }}}


{{{ graph( 600, 600, -10, 35, -25, 75, -0.8x^2 + 16.2x - 10) }}}