Question

when 30 orange trees are planted on an acre, each will produce 500 oranges per year. for every additional orange tree planted, each tree will produce 10 fewer oranges. how many total trees should be planted to maximize the yield?

Answer 1

40 trees per acre

Explanation:

: If x is the number of trees beyond 30 that are planted on the acre, then

the number of oranges produced will be: Oranges(x) = (number of trees) (yield per

tree) = (30 + x)(500 – 10x) = 15,000 + 200x – 10x

2

. The derivative Oranges'(x) =

200 – 20x is zero when x = 10. Using the second derivative test, Oranges"(x) = –

20 is negative, so this is maximal. Thus, x = 10 more than 30 trees should be

planted, for a total of 40 trees per acre.