The number of units that must be produced to make average cost a minimum is?

Question

Let C(x)= 0.3x^2+150 be the cost for producing x units. How man units must be produced in order for the average cost to be a minimum?

Answer 1

AC = C/x = .3x + 150/x

MC = .6x

AC is at a minimum when AC=MC. Average Cost is a U shaped curve, At the minimum point of the U shaped curve is where Marginal Cost intersects it.

.3x + 150/x = .6x

.3x = 150/x

.3x^2 = 150

x^2 = 150/.3 = 1500/3 = 500

x = 10sqr5 = about 22.36 = about 22 units to minimize average cost