A papaya grower estimates that if 20 trees are planted on his patch of land, each tree will average 60 kilograms of papaya per year. For each additional tree planted on his patch of land, the average yield per tree drops two kilograms. How many trees should be planted on the
grower’s land to maximize the yield ?
Answers
Given : If 20 trees are planted on his patch of land, each tree will average 60 kilograms of papaya per year.
For each additional tree planted on his patch of land, the average yield per tree drops two kilograms.
To Find : How many trees should be planted on the grower’s land to maximize the yield
Solution:
Assume that x trees more than 20 landed
Then Total tress = 20 + x
Yield = 60 - 2x kg
Total Yield Y(x) = (20 + x)(60 - 2x)
Y(x) = 1200 + 20x - 2x²
Y'(x) = 20 - 4x
Y'(x) = 0 => 20 - 4x = 0 => x = 5
Y''(x) = - 4 <0
Hence Maximum yield at x = 5
Total Tress Planted = 20 + 5 = 25
25 trees should be planted on the grower’s land to maximize the yield
Learn More:
find the local maximA or minima of the function: f(x)= sinx + cosx ...
brainly.in/question/21125629
examine the maxima and minima of the function f(x)=2x³-21x²+36x ...
brainly.in/question/1781825
Answer:
Assume that x trees more than 20 landed
Then Total tress = 20 + x
Yield=60-2x kg
Total Yield Y(x) = (20 + x)(60 - 2x)
Y(x) = 1200 + 20x - 2x ^ 2
Y'(x) = 20 - 4x
Y'(x) = 0 => 20 - 4x = 0 => x = 5
Y"(x) = = -4 <0
Hence Maximum yield at x = 5.
Total Tress Planted = 20 + 5 = 25.
25 trees should be planted on the grower's
land to maximize the yield.