Precalculus question

Question

Sylvia has an apple orchard. One season, her 100 trees yielded 140 apples per tree. She wants to increase her production by adding more trees to the orchard. However, she knows that for every 10 additional trees she plants, she will lose 4 apples per tree (i.e., the yield per tree will decrease by 4 apples). How many trees should she have in the orchard to maximize her production of apples?

Answer 1

The slope of the line for the relationship between trees and production has slope -2/5 and is

y=(1/5)(780-2x)

the production is P = (1/5)(780x-2x²)

production is maximized when 4x - 780 = 0 (i.e. when the derivative of production is 0)

You take it from here.