Answer:
She should have 200 trees
Step-by-step explanation:
Given,
Original number of trees = 100,
Also, original number of apples per tree = 120,
∵ for every 10 additional trees there is a lose 4 apples per tree,
i.e. if number of trees = 100 + 10x, apples per tree = 120 - 4x
Thus, the total apples = number of trees × apples per tree
Y(x) = (100 + 10x) × (120 - 4x)
Differentiating w. r. t. x,
Y'(x) = (100 + 10x)(-4) + (120 - 4x) (10) = -400 - 40x + 1200 - 40x = 800 - 80x
Again differentiating w. r. t. x,
Y''(x) = -80
For maxima or minima,
Y'(x) = 0
For x = 10,
Y''(x) = negative,
Hence, Y(x) is maximum at x = 10,
i.e. the number of trees for maximize the production = 100 + 10(10) = 100 + 100 = 200