Question

100 points!!!!!!!

Answer 1

Answer:

The minimum unit cost is equal to $15,339

Step-by-step explanation:

Let

x ----> the number of engines

C ---> the cost in dollars to make each airplane engine

we have

$C(x)=0.5x^{2} -100x+20,339$

This is a vertical parabola open upward (the leading coefficient is positive)

The vertex represent the minimum of the parabola

The minimum unit cost is equal to the y-coordinate of the vertex

Convert the quadratic equation into vertex form

Factor 0.5

$C(x)=0.5(x^{2} -200x)+20,339$

Complete the square. Remember to balance the equation by adding the same constants to each side

$C(x)=0.5(x^{2} -200x+100^2)+20,339-5,000$

$C(x)=0.5(x^{2} -200x+10,000)+15,339$

Rewrite as perfect squares

$C(x)=0.5(x-100)^{2}+15,339$ ----> equation into vertex form

The vertex is the point (100,15,339)

The y-coordinate of the vertex is 15,339

therefore

The minimum unit cost is equal to $15,339