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:
[tex]A(x)=\dfrac{C(x)}{x}=\dfrac{2x^2-3x+5}{x}=2x-3+5x^{-1}[/tex]
To optimize this function, we derive and equal to zero:
[tex]\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\\[/tex]
The average cost is minimized for x=1.58.
