AKI'S bicycyle designs has determined that when x hundreds bicycles are built the average cost per bike is given C(x)=0.1x^2-1.4x+10.766. Where C(x)is in hundreds of dollars. How many bicycles should the shop build to minimize the average cost per bicycle.
The shop should build bicycles.
C(x) = 0.1x^2 - 1.4x + 10.766.
The min. point on the parabola is the
vertex which represents min. cost:
V(x,C).
Xv = -B/2A = -1.4 / 0.2 = 7 Hundreds =
700 Bikes.
To find the number of bicycles the shop should build to minimize the average cost per bicycle, we need to find the minimum point of the quadratic function C(x) = 0.1x^2 - 1.4x + 10.766.
The minimum point of this quadratic function corresponds to the value of x where the average cost per bicycle is at its lowest. This point is called the vertex of the parabola.
The x-coordinate of the vertex can be found using the formula x = -b / (2a), where a and b are the coefficients of the quadratic equation.
In this case, the quadratic equation is C(x) = 0.1x^2 - 1.4x + 10.766, so a = 0.1 and b = -1.4.
Using the formula x = -b / (2a), we can find the x-coordinate of the vertex:
x = -(-1.4) / (2 * 0.1)
x = 1.4 / 0.2
x = 7
Therefore, the shop should build 7 hundred bicycles to minimize the average cost per bicycle.