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

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 = 10 (to be added)

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

                             = 12800 apple

maximum yield of the orchard is 12800 apple