An orange grove produces a profit of $ 100 per tree when there are 1300 trees planted. because of overcrowding, the profit per tree (for every tree in the grove) is reduced by 4 cents per tree for each one additional tree planted. how many trees should be planted in order to maximize the total profit of the orange grove? what is the maximum profit? how many trees should be planted in order to maximize the total profit of the orange grove?

Step-by-step explanation:

(x) = (1100 + x) (100 - .05(x-1100))

This is a quadratic, graphs as a parabola that opens downward. A maximum cam be found.

The zeros of the function are

(1100 + x) = 0 or [100 - .05(x-1100)] = 0

x = -1100 is the left x-intercept.

[100 - .05(x-1100)] = 0

100 = .05(x-1100)

2000 = x - 1100

x = 3100 is the right intercept.

Maximization of profits is at the mid point of the zeros (x-intercepts)

(3100 + -1100)/2 = 1000

1100 + 1000 = 2100 trees should be planted to maximize profits.

f(x) = (1100 + 1000) (100 - .05(1000-1100))

f(x) = (2000) (105) = 220,500 is the maximum profit.

I hope this helps!

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step-by-step explanation: