Get The Highest​ Yield With Trees and Bushels

Question

An apple farm yields an average of 45 bushels of apples per tree when 21 trees are planted on an acre of ground. Each time 1 more tree is planted per​ acre, the yield decreases by 1 bushel​ (bu) per tree as a result of crowding. How many trees should be planted on an acre in order to get the highest​ yield?

In order to get the highest​ yield, (blank) trees should be planted on an acre.

Answer 1

trees x (bushels per tree) = bushels of apples

(21+t) (45-t) = bushels of apples

-t^2 + 33t +945 = bushels of apples

This is a parabola opening down. The vertex occurs when t=-b/2a = -33/(-2) = 16.5 trees should be planted