SOLUTION: The monthly profit, P, in thousands of dollars, of a bicycle company can be estimated by the formula P=-2x(squared)+16X-12......where X is the number of bicycles, in hundreds, sold

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: The monthly profit, P, in thousands of dollars, of a bicycle company can be estimated by the formula P=-2x(squared)+16X-12......where X is the number of bicycles, in hundreds, sold      Log On


   

Question 82907: The monthly profit, P, in thousands of dollars, of a bicycle company can be estimated by the formula P=-2x(squared)+16X-12......where X is the number of bicycles, in hundreds, sold per month.
a) How many bicycles must be sold for maximum profit?
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?
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
P+=+-2x%5E2+%2B+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%5E2+%2B+16x+-+12
0+=+x%5E2+-+8x+%2B+6
-6+=+x%5E2+-+8x Quadratic Formula or Solving Squares
10+=+%28x+-+4%29%5E2
4+%2B-+sqrt%2810%29+=+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%28300%2C300%2C-2%2C12%2C-2%2C20%2C-2x%5E2+%2B+16x+-+12%29