Question

An aircraft factory manufactures airplane engines. The unit cost C (the cost in dollars to make each airplane engine) depends on the number of engines made. If x engines are made, then the unit cost is given by the function C(x)=x2-180x+20,482. How many engines must be made to minimize the unit cost? Do not round your answer.​

Answer 1

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:

$f(x) = ax^{2} + bx + c$

It's vertex is the point $(x_{v}, y_{v})$

In which

$x_{v} = -\frac{b}{2a}$

$y_{v} = -\frac{\Delta}{4a}$

Where

$\Delta = b^2-4ac$

If a>0, the minimum value of the function will happen for $x = x_v$

C(x)=x²-180x+20,482

This means that $a = 1, b = -180, c = 20482$

How many engines must be made to minimize the unit cost?

x value of the vertex. So

$x_{v} = -\frac{b}{2a} = -\frac{-180}{2(1)} = 90$

90 engines must be made to minimize the unit cost.