Suppose you own an apartment building containing 100 units. If you charge $400 per

month for each unit, then all units can be rented out. For every $20 increase in monthly rent, you

will lose one customer. What monthly rent should you charge to maximize your revenue? Show that

the corresponding revenue is an absolute maximum.

Attempt: (400+20x)(100-x)

40,000+1600x-20x^2

16000-40x

x=400

completing the square method:

(x+40)^2+400

both yield 400 as answer which would make max rent 8400 which is incorrect. IS my formula wrong? Where did i go wrong