Answer:
a. To maximize the annual yield for the acre the number of walnut to be planted per acre is n = 45
b. the maximum number of pounds of walnuts per acre is T = 4,050
Step-by-step explanation:
Let T represent the total number of pounds of walnuts per acre and n represent the number of trees per acre.
From the question;
For each additional tree over 20, the annual yield per tree for all trees on the acre decreases by 2 pounds due to overcrowding
The number of walnut yield per tree can be represented as;
x = 140 - (n-20)2
the total number of pounds of walnuts per acre T is;
T = n(x)
T = n(140 - (n-20)2) = 140n - 2n(n-20) = 140n - 2n^2 + 40n
T = 180n - 2n^2
Maximizing T, we will differentiate T.
T is maximum at dT/dn = 0
dT/dn = 180 - 4n = 0
4n = 180
n = 180/4 = 45
Substituting the value of into the equation of T;
T = 180(45) - 2(45^2)
T = 4,050
Therefore,
a. To maximize the annual yield for the acre the number of walnut to be planted per acre is n = 45
b. the maximum number of pounds of walnuts per acre is T = 4,050
