Question

The yield in bushels from a grove of orange trees is given by Y = x(600 − x), where x is the number of orange trees per acre. How many trees will maximize the yield?

Answer 1

Answer:

90000

Step-by-step explanation:

Y = x(600 - x)

Let's rearrange the equation so that we have

Y = x(-x + 600)

Y = -x² + 600

When you take a look at parabolas, we know that their maximum or minimum values are usually on the axis of symmetry. This axis of symmetry has an equation of

x = -b/2a,

In this question, the axis of symmetry is

x = -600 / -2

x = 300

This means that planting 300 trees will maximize your yield. If you substitute for x = 300 into the equation, the maximum yield will be

y = 300 (600 - 300)

y = 90000.