SOLUTION: Al Bike shop design has determined that when x hundred bikes are built the average cost per bike is C(x)=0.6x^2-1.3x+5.971, when C(x)is hundreds of dollars. How many bikes should b

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Al Bike shop design has determined that when x hundred bikes are built the average cost per bike is C(x)=0.6x^2-1.3x+5.971, when C(x)is hundreds of dollars. How many bikes should b      Log On


   

Question 176016: Al Bike shop design has determined that when x hundred bikes are built the average cost per bike is C(x)=0.6x^2-1.3x+5.971, when C(x)is hundreds of dollars. How many bikes should be built in order to have minimum cost?
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
C(x)=0.6x^2-1.3x+5.971
Where 'x' is hundreds of bikes
.
Since this is a "parabola" with a POSITIVE 'a' coefficient of (0.6) we know that it opens upwards -- therefore, the "vertex" of the parabola will give you the "minimum".
.
The x coordinate = -b/2a
Substituting our values:
The x coordinate = -(-1.3)/(2(.6))
The x coordinate = (1.3)/(1.2) = 1.083 "hundreds of bikes"
.
Therefore, building
108 bikes -- minimizes costs