Homework SourseThe annual yield per walnut tree is fairly constant at 100 p
The annual yield per walnut tree is fairly constant at 100 pounds per tree when the number or trees per acre is 20 or fewer. For each additional tree over 20, the annual yield per tree for all trees on the acre decreases by 2 pounds due to overcrowding. How many walnut trees should be planed per acre to maximize the annual yield for the acre? What is the maximum number of pounds of walnuts per acre?
Solution
F(x)= (100- 2x)(20+x) where x is the number of trees over twenty F(x)= 2000 +60 x -2x^2 Vertex is at x= -b/2a= -60/-4= 15 So 20 +15= 35 walnut trees should be planted. Max pounds per acre 35* 70= 2,450.
