Question

A Florida citrus grower estimates that if 60 orange trees are planted, the average yield per tree will be 400 oranges. The average yield per tree will decrease by 4 oranges for each additional tree planted on the same acreage. How many trees should the grower plant to maximize the total yield?

Answer 1

Total yield = Avg yield * num of Trees

Avg yield is 400 when n=60 but goes down by 4 for each additional tree
---> 400 - 4(n-60)

\[Y = n(400-4(n-60))\]
\[Y = 640n -4n^2\]
Maximize by setting derivative equal to 0
\[\frac{dY}{dn} = 640 - 8n = 0\]
\[n = 80\]