Question

the yield in bushels from a grove of orange trees is given by y = x(200 − x), where x is the number of orange trees per acre. how many trees will maximize the yield?

Answer 1

To maximize the yield of a grove of orange trees, we need to find the number of trees that will give the highest possible yield. This can be done by using the vertex formula of a parabola.

Step-by-step explanation:

The yield in bushels from a grove of orange trees is given by the equation: y = x(200 - x), where x is the number of orange trees per acre. To maximize the yield, we need to find the value of x that gives the highest possible value of y.

To find the maximum, we can use the vertex formula of a parabola: x = -b / (2a). In this case, a = -1 and b = 200, so the formula becomes x = -200 / (2(-1)) = -200 / -2 = 100.

Therefore, the number of trees that will maximize the yield is 100.