# Math Help - Maximization/Word Problem

1. ## Maximization/Word Problem

An apple orchard has an average yield of 32 bushels of apples/tree if tree density is 20 trees/acre. For each unit increase in tree density, the yield decreases by 4 bushels/tree. How many trees should be planted in order to maximize the yield?

Can anyone help explain how to set this problem up/solve it? Thanks!!!

2. Originally Posted by Chrisss
An apple orchard has an average yield of 32 bushels of apples/tree if tree density is 20 trees/acre. For each unit increase in tree density, the yield decreases by 4 bushels/tree. How many trees should be planted in order to maximize the yield?
let $x$ = number of unit increases in tree density

$y$ = yield in bushels per acre

yield = (bushels per tree)(trees per acre)

$y = (32-4x)(20+x)$