Answer:
90 engines must be made to minimize the unit cost.
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, y_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
Where
[tex]\Delta = b^2-4ac[/tex]
If a>0, the minimum value of the function will happen for [tex]x = x_v[/tex]
C(x)=x²-180x+20,482
This means that [tex]a = 1, b = -180, c = 20482[/tex]
How many engines must be made to minimize the unit cost?
x value of the vertex. So
[tex]x_{v} = -\frac{b}{2a} = -\frac{-180}{2(1)} = 90[/tex]
90 engines must be made to minimize the unit cost.
