The number of oranges produced by each tree in an orange grove depends on how densely the trees are planted. If n trees are planted on an acre of land, then each tree produces oranges. So the number of oranges produced per acre is What is the maximum yield of the trees, and how many trees should be planted per acre to obtain the maximum yield of oranges? (Rounded to the nearest whole number)
A) Maximum yield of the trees is 625 oranges when 9 trees are planted
B) Maximum yield of the trees is 10,851 oranges when 35 trees are planted
C) There is no maximum yield of the trees
D) Maximum yield of the trees is 7,350 oranges when 15 trees are planted
E) Maximum yield of the trees is 27,500 oranges when 100 trees are planted

Question

The number of oranges produced by each tree in an orange grove depends on how densely the trees are planted. If n trees are planted on an acre of land, then each tree produces  oranges. So the number of oranges produced per acre is  What is the maximum yield of the trees, and how many trees should be planted per acre to obtain the maximum yield of oranges? (Rounded to the nearest whole number)
A) Maximum yield of the trees is 625 oranges when 9 trees are planted 
B) Maximum yield of the trees is 10,851 oranges when 35 trees are planted 
C) There is no maximum yield of the trees 
D) Maximum yield of the trees is 7,350 oranges when 15 trees are planted 
E) Maximum yield of the trees is 27,500 oranges when 100 trees are planted

Quizplus · Accepted Answer

To find the maximum yield of oranges, we need to find the vertex of the parabola representing the number of oranges produced. The equation of the parabola is y = -11.25n^2 + 472.5n, where n is the number of trees planted. To find the vertex, we can use the formula n = -b/2a, where a = -11.25 and b = 472.5. Plugging in these values, we get n = -472.5/(2*-11.25) = 21. Therefore, the maximum yield is obtained when 35 trees are planted, and the yield is 10,851 oranges (rounded to the nearest whole number).

The Number of Oranges Produced by Each Tree in an Orange