Question

a florida citrus grower estimates that if 60 orange trees are planted, the average yield per tree will be 400 oranges. The average yield will decrease by 4 oranges per tree for each additional tree planted on the same acreage. Express the grower's total yield as a function of the number of additional trees planted, draw the graph and estimate the total number of trees the grower should plant to maximize yield.

Answer 1

Answer: 80 trees

Step-by-step explanation: just bc it is

Answer 2

Answer: 80 trees

Explanation:

YIELD = (NUMBER OF TREES)*(NUMBER OF ORANGES PER TREE)

Let's assume NUMBER OF TREES = 60 + x, where x is the number of additional trees above 60

The NUMBER OF ORANGES PER TREE will = (400-4x). Hence:

YIELD = (60+x)*(400-4x) = 24000-240x+400x-4x2 = -4x2 + 160x + 24,000

To find the maximum YIELD, take the derivative of YIELD wrt x, set it to zero, and solve for x:

d(YIELD)/dx = -8x + 160

0 = -8x +160

8x = 160

x = 20

The grower should grow 60 + 20 = 80 trees to maximize yield.