Question 332126
P(x)= - 0.08x^2 + 60x - 750 how many units will give a break even point for this product? 
:
Break-even point is when profit is 0, therefore
-.08x^2 + 60x - 750 = 0
using the quadratic formula; {{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
in this problem: a=-.08. b=60, c=-750
{{{x = (-60 +- sqrt(60^2- 4 *-.08*-750 ))/(2*-.08) }}}
:
{{{x = (-60 +- sqrt(3600-240 ))/(-.16) }}}
:
{{{x = (-60 +- sqrt(3360 ))/(-.16) }}}
Two solutions, but we want the lowest value here
{{{x = (-60 + 58)/(-.16) }}}
x = {{{(-2)/(-.16)}}}
x = +12.5, ~ 13 units to break even (a slight profit, integer units required)
;
:
Check in the original equation
-.08(13^2) + 60(13) - 750 = +$43.52, a slight profit