The average cost is given by the next equation:
[tex]C(x)=0.1x^2-0.5x+5.582[/tex]
The graph of the function is
As we can see the parabola opens upwards therefore the minim will be located in the vertex
[tex]x=\frac{-b}{2a}[/tex]
in our case
b=-0.5
a=0.1
[tex]x=\frac{0.5}{2(0.1)}=2.5[/tex]
2.5 hundred
Then
[tex]2.5\times100=250[/tex]
Therefore, the shop should build 250 bicycles
