If the total cost function for a product is Cx 250 01x2 do

If the total cost function for a product is C(x) = 250 + 0.1x^2 dollars producing how many units, x, will result in a minimum average cost per unit? x = units Find the minimum average cost per unit. $

C(x) = 250 + 0.1x²

Let: Average Cost = AC

AC(x) = (250 + 0.1x²) / x = 250/x + 0.1x

For the Average Cost is a minimum, d(AC)/dx = 0 = -250/x^2 + 0.1 ====> x = 50

At x = 50 ===> AC(50) = 250/50 + 0.1*50 = 10