Question

A farmer is planting a small orchard. He is advised that if he plants up to 60 trees of a particular type, average harvest from each tree will be about 120 kg, but for each additional tree planted the expected yield will go down by an average of 2 kg per tree due to overcrowding. How many trees should he plant in order to produce the maximum yield of fruit?

Answer 1

Let the number of extra trees be x. Then the total yield y is

y=(60+x)(120-2x)

Now just find where y'=0 to get the maximum yield