An orange grove now has 40 trees per acre with an average yield of 1000 oranges per tree. It is observed that for each additional tree planted per acre, the yield per tree is reduced by 20 oranges. What is the maximum yield per acre that the grove will produce? Make careful arguments that show you indeed have the maximum value.
Source: Rosenberg, R.L. (1984). Elementary Calculus: Course Notes. Ottawa, Canada: Holt, Rinehart and Winston. (Exercise 2: Question 13, p. 11)