Question

An orchard contains 30 apple​ trees, each of which yields about 450 apples over the growing season. The owner plans to add more​ trees, but each new tree will reduce the average yield per tree by about 8 apples over the season. How many trees should be added to maximize the total yield of​ apples? What would be the maximum yield for the apple orchard for the​ season?

Answer 1

Answer

given,

apple tree in orchard = 30

yield of apple =  450 apples

yield reduced per tree = 8 apples

number of trees added be x

trees added to maximize the yield = ?

total yield = (30 + x)(400 - 8 x )

T = 12000- 240 x  + 400 x - 8 x²

T = - 8 x² + 160 x + 12000

max will occur when

$x = \dfrac{-b}{2a}$

$x = \dfrac{-160}{2(-8)}$

x = 10 (to be added)

maximum yields =  - 8 (10²) + 160 x 10 + 12000

                             = 12800 apple

maximum yield of the orchard is 12800 apple