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
[tex]C(x)=0.5x^{2} -100x+20,339[/tex]
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
[tex]C(x)=0.5(x^{2} -200x)+20,339[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side
[tex]C(x)=0.5(x^{2} -200x+100^2)+20,339-5,000[/tex]
[tex]C(x)=0.5(x^{2} -200x+10,000)+15,339[/tex]
Rewrite as perfect squares
[tex]C(x)=0.5(x-100)^{2}+15,339[/tex] ----> 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
