Answer:
Number of orange trees = 3528
Step-by-step explanation:
Given: Average annual orange yield = 124 pounds (lbs) per tree
Number of trees = 22 per acre
Each tree produces 124 pounds, so 22 trees will produce
124*22 = 2728 lbs per acre
For every additional tree over 22, 2 pounds per tree is lost.
So, if you add x trees, you lose 2x pounds.
Thus, we have the function:
f(x) = (124 - 2x)*(22 + x) for the added tree(s)
For quadratic equations like this, the maximum(or minimum) is obtained by substituting x= -b/2a into the given equation. a and b are obtained from the general form of a quadratic equation:
Comparing this with f(x), we have that
a = -2 (coefficient of x2)
b = 80 (coefficient of x)
Using these values in x = -b/2a, we get
So, use x = 20 in the maximum function we got earlier
Therefore, the number of oranges that should be planted in order to maximize the number of pounds of oranges per acre = 3528
