The annual yield per walnut tree is fairly constant at 60 pounds per tree when the number of 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. Therefore, assuming that the number of walnut trees per acre is greater than 20,the annual yield of walnuts on the acre, A, as a function of the number of walnut trees, t, is the following:

Question

The annual yield per walnut tree is fairly constant at 60 pounds per tree when the number of 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. Therefore, assuming that the number of walnut trees per acre is greater than 20,the annual yield of walnuts on the acre, A, as a function of the number of walnut trees, t, is the following:
A(t) = −2t^2 + 100t 
(a) How many walnut trees should be planted per acre to maximize the annual yield for the acre?
(b) What is is the maximum number of pounds of walnuts per acre?

oobleck · Answer

Recall that for the parabola y = ax^23+bx+c,
(a) The vertex is at x = -b/2a
(b) evaluate y at that value of x.

Or, think of the vertex form for this parabola
A(t) = -2(t-25)^2 + 1250
The vertex is at (25,1250)