Question 82907
{{{P = -2x^2 + 16x - 12}}}
a) How many bicycles must be sold for maximum profit?
This is a vertical parabola that is opening downward. The vertex will be the maximum point for P.
v(-b/(2a),f(x))
v(-16/(-4),f(x))
v(4,f(4))
v(4,20) or $20,000 dollars
b) What is the minimum number of bicycles that must be sold to break even?
c) What is the maximum number of bicycles that must be sold to break even?
{{{0 = -2x^2 + 16x - 12}}}
{{{0 = x^2 - 8x + 6}}}
{{{-6 = x^2 - 8x}}} Quadratic Formula or Solving Squares
{{{10 = (x - 4)^2}}}
{{{4 +- sqrt(10) = x}}}
Min: 4 - sqrt(10) = 0.8377.... or about 1 which is 100 bikes
Max: 4 + sqrt(10) = 7.1622.... or about 7 which is 700 bikes
~ Proof ~
{{{graph(300,300,-2,12,-2,20,-2x^2 + 16x - 12)}}}