Question

The cost function is given by C(x) = 2x 2− 3x + 5, where x is the number of items produced. For what value of x is the AVERAGE cost function minimized?

Answer 1

Answer:

The average cost is minimized for x=1.58.

Step-by-step explanation:

The cost function is C(x) = 2x 2− 3x + 5, where x is the number of items produced.

The average cost is C(x)/x, that is the total cost divided by the units produced.

Then the average cost function A(x) becomes:

$A(x)=\dfrac{C(x)}{x}=\dfrac{2x^2-3x+5}{x}=2x-3+5x^{-1}$

To optimize this function, we derive and equal to zero:

$\dfrac{dA}{dx}=0\\\\\\\dfrac{dA}{dx}=2+5(-1)x^{-2}=0\\\\\\2-5x^{-2}=0\\\\x^{-2}=2/5\\\\x^2=5/2\\\\x=\sqrt{5/2}\approx1.58114$

The average cost is minimized for x=1.58.