A firm has the average cost equation AC=10- 1/3q +1/180q^2. when output=0, AC is 10. When output= 30 average cost is minimized at 5 dollars.

Suppose the owner buys another similar plant, so the business now has two of the same plants, what is the Average cost curve for the expanded operation?

I think the new AC function will be AC=20 - 1/3q +1/180q^2. Correct?

Also, prove that the output level at which it pays to switch from one plant to two plants is q=40