Question

A farmer finds that if she plants 25 trees per acre, each tree will yield 41 bushels of fruit. She estimates that for each additional tree planted per acre, the yield of each tree will decrease by 1 bushel. How many trees should she plant per acre to maximize her harvest?

Answer 1

17

Explanation:

Let F be the number of fruit per acre

F = (25 + x) × (41 - x)

F=1025 -25x + 41x -x²

F=-x²+16x+1025

The maximum yield is at the maximum of that expression, which is at

`x=-(b)/(2a) =>-(16)/(-2*1)`

x=8

So apparently she currently has far too many trees per acre. To get the maximum yield, she needs to reduce the number of trees per acre by 8.

So the number of trees per acre for maximum yield is 25-8 = 17.