Respuesta :
Answer:
About 89 bicycles.
Step-by-step explanation:
Let C(x) is average cost (in hundreds of dollars) per bicycle and x be the number bicycles built (in hundred).
[tex]C(x)=0.9x^2-1.7x+10.861[/tex]
We need to find the number of bicycles for which the average cost per bicycle is minimum.
The vertex form of a parabola is
[tex]f(x)=a(x-h)^2+k[/tex] .... (1)
where, a is constant and (h,k) is vertex.
[tex]C(x)=(0.9x^2-1.7x)+10.861[/tex]
Taking out 0.9 from the parenthesis.
[tex]C(x)=0.9(x^2-1.889x)+10.861[/tex]
If an expression is [tex]x^2+bx[/tex], then we add [tex](\frac{b}{2})^2[/tex] in the expression to make it perfect square.
Here, b=-1.889,
[tex](\frac{b}{2})^2=(\frac{-1.889}{2})^2=0.892[/tex]
Add an d subtract 0.892 in the parenthesis.
[tex]C(x)=0.9(x^2-1.889x+0.892-0.892)+10.861[/tex]
[tex]C(x)=0.9(x^2-1.889x+0.892)+0.9(-0.892)+10.861[/tex]
[tex]C(x)=0.9(x^2-0.892)^2-0.8028+10.861[/tex]
[tex]C(x)=0.9(x^2-0.892)^2+10.0582[/tex] ... (2)
From (1) and (2) we get
[tex]h=0.892,k=10.0582[/tex]
Aki should built 0.892 hundred bicycle to minimize the average cost per bicycle.
[tex]0.892\times 100=89.2\approx 89[/tex]
Therefore, the Aki should built 89 bicycle to minimize the average cost per bicycle.
