Question

The cost function is C(x)=10000+5x+1/9x^2. Determine the value of x that gives a minimum average cost. (C(x)/x)

Answer 1

C(x)=10000+5x+1/9x^2.

C(x) is a quadratic function (parabolic shape), so the minimum value corresponds to the x-value of the vertex's point.

We find vertex using the fact that the vertex has coordinate x=−b/2a

On this case b = 5

and a =1/9

So, x = -45/2 = −22.5