Question

The annual yield per walnut tree is fairly constant at 120 pounds per tree when the number of trees per acre is 30 or fewer. For each additional tree over 30​, the annual yield per tree for all trees on the acre decreases by 2 pounds due to overcrowding. How many walnut trees should be planted per acre to maximize the annual yield for the​ acre? What is the maximum number of pounds of walnuts per​ acre?

Answer 1

Answer:

The maximum number of pounds of Walnuts per acre is 3150.

Explanation:

F(x) = (120- 2x)(30+x)  where x is the number of trees over 30.

F(x) = 3600 + 60 x -2x^2

Vertex is at x = -b/2a = -60/-4 = 15

So 30 + 15= 45 walnut trees should be planted.

Max pounds per acre 45×70 = 3150.

Therefore, the maximum number of pounds of Walnuts per acre is 3150.